The number of surjections from A = 1 , 2 . . . . , n , n ≥ 2 onto B = a , b is

If f ( y ) = y 1 – y 2 , g ( y ) = y 1 + y 2 , then (fog)(y) is equal to

The range of f ( x ) = cos − 1 log 4 x − π 2 + sin − 1 1 + x 2 2 x is equal to

The domain of the function f ( x ) = sin − 1 ( 3 − x ) ln ( | x | − 2 ) is

Given the function f ( x ) = a x + a − x 2 (where a > 2 ). Then f ( x + y ) + f ( x − y ) =

The function f : R R given by f ( x ) = 3 – 2 sin x is

The domain of the function f ( x ) = sin − 1 ( x − 3 ) 9 − x 2 is

Let R be a relation defined on the set of real numbers by a R b ⇔ 1 + a b > 0 . Then R is

Let P = ( x , y ) ∣ x 2 + y 2 = 1 , x , y ∈ R . Then, P is

Which one of the following relations on R is an equivalence relation?

Let R be a relation on a set A such that R = R − 1 , then R is

The domain of definition of the function f ( x ) given by the equation 2 x + 2 y = 2 is

The domain of definition of the function f ( x ) = sin − 1 ( 2 x ) + π 6 for real-valued x is

Let R be the relation on the set of all real numbers defined by a R b iff | a − b | ≤ 1 . Then, R is

The domain of the function f ( x ) = log 3 + x x 2 − 1 is

Let f ( x ) = ( x + 1 ) 2 − 1 , x ≥ − 1 . Then the set x : f ( x ) = f − 1 ( x ) is

Find the range of the function f ( x ) = x + x 2

If f ( x ) = sin x + cos x , g ( x ) = x 2 − 1 , then g ( f ( x ) ) is invertible in the domain

the relation R in the set R of real numbers, defined as R = ( a , b ) : a ≤ b 2 is

Which of the following functions is periodic?

If the period of cos ( sin ( n x ) ) tan x n , n ∈ N , is 6 π , then n =

Find the domain of the function f ( x ) = x − 3 ( x + 3 ) x 2 − 4

The range of the y = x 2 − 4 is

The range of f ( x ) = sgn x 2 − 2 x + 3 i s

The domain of f(x) = log { x } , (where { } represents the fractional part function).

if a,b,c are non-zero rational numbers then the sum of all the possible values of a a + b b + c c

The domain of f ( x ) = sin x + 16 − x 2 is

The domain of the function 1 1 + 2 sin x is

The range of f ( x ) = log 3 5 − 4 x − x 2 is

The domain of f(x) = sin − 1 [ x ] (where [ ] represents the greatest integer function).

Domain of definition of the function f ( x ) = log ( | x | − 1 ) x 2 + 4 x + 4 is

Let P = x , y | x 2 + y 2 = 1 , x , y ∈ R . Then P is

Which one of following best represent the graph of y = x log , π ?

The domain of the function f x = sin x + cos x + 7 x – x 2 – 6 is

If R ⊂ A × B and S ⊂ B × C be two relations, then ( SoR ) – 1 =

Let X be a family of set and R be a relation on X defined by ‘A is disjoint from B’. Then R is

x 2 = xy is a relation which is

n/m means that n is factor of m, then the relation f is

If f ( x ) = cos 2 x + sin 4 x sin 2 x + cos 4 x for x ∈ R then f ( 2018 ) =

The domain of the function f ( x ) = cos log 16 − x 2 3 − x is

The domain of the function f ( x ) = 24 − x C 3 x − 1 + 40 − 6 x C 8 x − 10 is ,

The domain of the function f ( x ) = log 1 / 2 x − 1 2 + log 2 4 x 2 − 4 x + 5 is

The domain of definition of the function y (x) given by the equation 2 x + 2 y = 2 is

If g [ f ( x ) ] = | sin x | and f [ g ( x ) ] = ( sin x ) 2 , then

The period of the function f (x) = cos x 2 is

The domain of the function f ( x ) = log 10 1 − log 10 x 2 − 5 x + 16 is

The domain of the function f ( x ) = log x + 1 2 x 2 − 5 x + 6 is

If f : R R, g : R R be two given functions then f (x) = 2 min { f (x) – g (x), 0} equals

The domain of the function f ( x ) = 1 | sin x | + sin x is

Let f : R R be a function defined by, f ( x ) = x + x 2 , then f is

The solution of 8 x ≡ 6 ( mod 14 ) is where [ a ] = { a + 14 k : k ∈ I }

The relation ‘less than’ on the set of natural numbers is

If f : R R , f ( f ( x ) ) = ( f ( x ) ) 2 , then f f f ( x ) is not equal to

The range of the function f ( x ) = tan π 2 9 − x 2 is

Range of the function f ( x ) = cos − 1 log 4 x − π 2 + sin − 1 1 + x 2 4 x is

If ∑ k = 0 n f ( x + k a ) = 0 , where a > 0 , then the period of f ( x ) i s

Range of function f ( x ) = log 2 π + 2 sin − 1 3 − x 7 π is

The function f : ( − ∞ , − 1 ) 0 , e 5 defined by f ( x ) = e x 3 − 3 x + 2 is

f : R R defined by f ( x ) = 1 2 x | x | + cos x + 1 is

Period of f ( x ) = cos ( | sin x | − | cos x | ) is

If g ( x ) = x 2 + x − 2 and 1 2 ( gof ) ( x ) = 2 x 2 − 5 x + 2 , then f ( x ) is equal to

Which of the following functions is an injective (one-one) function in its respective domain?

The range of the function y = 1 x 2 + 2

The domain of f ( x ) = sin − 1 x 2 2 is

Number of integral values of x satisfyng the inequality 3 4 6 x + 10 – x 2 < 27 64 i s

Find the range of f(x) f ( x ) = sin − 1 [ x ]

The function f is continuous and has the property f(f(x))=1-x, then the value of f 1 4 + f 3 4 i s

The relation R defined on the set N of natural numbers by x R y ⇔ 2 x 2 − 3 x y + y 2 = 0 is

Let f ( x ) = x 3 − 1 , x < 2 x 2 + 3 , x ≥ 2 . Then

The number of linear functions f satisfying f ( x + f ( x ) ) = x + f ( x ) ∀ x ∈ R is

If f ( x ) = sin x + cos x , g ( x ) = x 2 − 1 , then g ( f ( x ) ) is invertible in the domain

The domain of definition of the function f x given by the equation 2 x + 2 y = 2 is

The domain of the following function is f x = log 2 – log 1 / 2 1 + 1 x 1 / 4 – 1

The exhaustive domain of the following function is f x = x 12 – x 9 + x 4 – x + 1

The range of the following function is f x = 1 – cos x 1 – cos x 1 – cos x . . . . ∞

Let R be the relation on the set R of all real numbers defined by a R b if a – b ≤ 1 . Then R is

Let R be a relation defined by R={(a,b):a≥b}, where a and b are real numbers, then R is

Let A = x , y , z , B = u , v , w and f : A B be defined by f(x)=u, f(y)=v, f(z) = w. Then f is

In the set X = a , b , c , d , which of the following functions in X ?

If f : R R is defined by f ( x ) = 2 x + x , then f 3 x – f – x – 4 x equals

The domain of the function f ( x ) = sin – 1 ( sin x ) – cos – 1 ( cos x ) in 0 , 2 π is

The domain of the function f ( x ) = x − 1 − x 2 is

The domain of the function f ( x ) = cos − 1 1 − | x | 2 is

The domain of the function f (x) = log 2 log 3 log 4 x is

The domain of definition of f ( x ) = 1 − | x | 2 − | x | is

The domain of the function f ( x ) = cos − 1 2 − | x | 4 + [ log ( 3 − x ) ] − 1 is

The domain of the function f ( x ) = e sin − 1 log 16 x 2 is

The domain of the function f ( x ) = 1 [ x ] 2 − [ x ] − 6 is

The range of the function f ( x ) = 3 x 2 − 4 x + 5 is

The range of the function y = 3 sin π 2 16 − x 2 is

The value of the function f ( x ) = x 2 − 3 x + 2 x 2 + x − 6 lies in the interval

The domain of the function f ( x ) = cot − 1 x x 2 − x 2 , x ∈ R is

The function f : R R defined by, f (x) = 4 x + 4 |x| is

Let f (x) = (–1) [x] (where [ . ] denotes the greatest integer function), then

Let f : [4, ∞) [4, ∞) be a function defined by, f (x) = 5 x(x – 4) , then f –1 (x) is

Let f be a function with domain [–3, 5] and let g (x) = |3x + 4|. Then the domain of ( fog) (x) is

The period of the function f (x) = a sin kx + b cos kx is

The period of the function f ( x ) = cos πx n ! − sin πx ( n + 1 ) ! is

The period of the function f ( x ) = | sin x | − | cos x | | sin x + cos x | is

The period of the function f ( x ) = tan x is

Which of the following functions has period π ?

The function f (x) = k |cos x| + k 2 |sin x| + ϕ (k) has period π 2 if k is equal to

The period of the function f ( x ) = 1 , when x is a rational 0 , when x is irrational is

The period of the function f (x) = x [x] is

If f ( x ) = x 2 + 1 [ x ] , ([⋅] denotes the greatest integer function), 1 ≤ x < 4, then

If 3 f ( x ) + 5 f 1 x = 1 x − 3 , ∀ x ( ≠ 0 ) ∈ R , then f (x) =

If f : R R , defined by f (x) = x 3 + 7, then the value of f –1 (71) and f –1 (–1) respectively are

The domain of the function f ( x ) = sin x x – x is

Let f ( x ) = a x + b , x ∈ R , a n d g ( x ) = x + d , x ∈ R , then f o g = g o f if and only if

The domain of the function f ( x ) = log 2 sin x is

The function f ( x ) = sin πx n ! – cos πx ( n + 1 ) ! is

A function out of the following whose period is not π is

Which of the following functions is an odd function

Let f ( x ) = ( x + 1 ) 2 – 1 ( x ≥ – 1 ) . Then the set S = { x : f ( x ) = f – 1 ( x ) } contains

Let R be a relation on a set A such that R = R − 1 then R is

If f ( x + 3 y , x − 3 y ) = 12 x y , then f ( x , y ) is

The domain of the function f ( x ) = sin − 1 log 3 x 3 is

Let f : R R be a function defined by f ( x ) = e | x | − e − x e x + e − x . Then

The domain of the function f ( x ) = − log 0.3 ( x − 1 ) − x 2 + 2 x + 8 is

Which of the following functions is not onto

The inverse function of f ( x ) = 8 2 x – 8 – 2 x 8 2 x + 8 – 2 x , x ∈ ( – 1 , 1 ) , is

The domain of definition of the function y = 1 log 10 1 – x + x + 2 is

The number of real solutions of the equation ( 9 / 10 ) x = – 3 + x – x 2 is

Complete set of range of the function f ( x ) = 1 x 6 + | x | 3 − 1 is equal to

If a f ( x ) + b f 1 x = x − 1 , x ≠ 0 , a ≠ b , then f ( 2 ) =

Let the function f : R R be defined by f ( x ) = 2 x + sin x for x ∈ R . Then f is

Let R be a relation on the set N be defined by { ( x , y ) ∣ x , y ∈ N , 2 x + y = 41 } . Then, R is

The void relation on a set A is

The domain of f ( x ) = 1 x – 1 x – 2 1 – 2 x is

The domain of | x − 2 | − 1 is

The domain of definition of the function f ( x ) given by the equation 2 x + 2 y = 2 is

The range of the function f ( x ) = tan π 2 9 − x 2 is

The domain of definition of f ( x ) = log 2 ( x + 3 ) x 2 + 3 x + 2 is

The range of the function f ( x ) = | x − 1 | + | x − 2 | , − 1 ≤ x ≤ 3 , is

Let f ( x ) = α x ( x + 1 ) , x ≠ − 1 . Then for what value of α is f ( f ( x ) ) = x ?

If f : [ 1 , ∞ ) [ 2 , ∞ ) is given by f ( x ) = x + 1 x , then f − 1 ( x ) equals

Let the function f : R R be defined by f ( x ) = 2 x + sin x for x ∈ R . Then f is

If f x 2 − 6 x + 6 + f x 2 − 4 x + 4 = 2 x ∀ x ∈ R then f ( − 3 ) + f ( 9 ) − 5 f ( 1 ) =

The domain of the function f ( x ) = 1 10 C x − 1 − 3 × 10 C x c o n t a i n s t h e p o i n t s

If f ( x ) = x , x is rational 1 − x , x is irrational , then f ( f ( x ) ) is

If f ( x ) = x 2 sin π x 2 , | x | < 1 x | x | , | x | ≥ 1 , then f ( x ) is

If f ( x ) is an invertible function and g ( x ) = 2 f ( x ) + 5 , then the value of g − 1 ( x ) is

If f ( x ) = maximum x 3 , x 2 , 1 64 ∀ x ∈ [ 0 , ∞ ) , then

Let g ( x ) = f ( x ) − 1 . If f ( x ) + f ( 1 − x ) = 2 ∀ x ∈ R , then g ( x ) is symmetrical about

Let g ( x ) = f ( x ) − 1 . If f ( x ) + f ( 1 − x ) = 2 ∀ x ∈ R , then g ( x ) is symmetrical about

The relation ‘less than’ on the set of natural numbers is

Let R be a relation on a set A such that R = R − 1 , then R is

Let P = ( x , y ) ∣ x 2 + y 2 = 1 , x , y ∈ R . Then, P is

Let R be a relation on the set N be defined by { ( x , y ) ∣ x , y ∈ N , 2 x + y = 41 } . Then, R is

The void relation on a set A is

Which one of the following relations on R is an equivalence relation?

The domain of f ( x ) = x 2 + | x + 3 | + x x + 2 − 1 is

The domain of | x − 2 | − 1 + 3 − | x − 2 | is

The domain of definition of the function y = 1 log 10 ( 1 − x ) + x + 2 is

The domain of definition of f ( x ) = log 2 ( x + 3 ) x 2 + 3 x + 2 is

The domain of the definition of the function f ( x ) = log 4 log 5 log 3 18 x − x 2 − 77 is

Let f ( x ) = cos − 1 x 2 1 + x 2 . The range of f is

The domain of f ( x ) = log | log x | is

If f ( x ) = 1 ( x + 1 ) e x − 1 ( x − 4 ) ( x + 5 ) ( x − 6 ) , then the domain of f ( x ) is

If f ( x ) = cos log e x , then f ( x ) f ( y ) − 1 2 f x y + f ( x y ) h a s v a l u e

Range of the expression f ( x ) = x 3 + x 2 + x − 3 x − 1 is

Let f ( x ) = 9 x 9 x + 3 . Then f ( x ) + f ( 1 − x ) =

Let f ( x ) = min . { 4 x + 1 , x + 2 , − 2 x + 4 } . Then the maximum value of f ( x ) is

If f ( x + 2 a ) = f ( x − 2 a ) , then f ( x ) is

The period of the function sin 3 x 2 + cos 5 x 5 is

What is the fundamental period of f ( x ) = sin x + sin 3 x cos x + cos 3 x ?

If f and g arc one-one functions, then

If f ( x ) = sin ( [ x ] π ) x 2 + x + 1 , where [.] denotes the greatest integer

If f ( x ) = 2 − x ; x < 0 x 2 − 4 x + 2 ; x ≥ 0 , then the value of f ( f ( f ( 1 ) ) ) i s

If f ( x ) = 5 log 5 x then f − 1 ( α − β ) where α , β ∈ R is equal to

If f ( x ) = x 1 + x 2 , then ( fofof ) ( x ) =

Find the domain of the function f ( x ) = x − 3 ( x + 3 ) x 2 − 4

Find the domain of the function f ( x ) = 1 | x − 2 | − ( x − 2 )

The range of the y = 9 − x 2 is

The range of the function y = x 2 − 2 x + 10 is

The range of the function f ( x ) = 1 − x 2 x 2 + 3 is

The range of f ( x ) = sin 2 x − sin x + 1 i s

The domain of f ( x ) = cos ( sin x ) is

The range of tan − 1 2 x 1 + x 2 is

Find the range of f ( x ) = cot − 1 2 x − x 2 .

The domain of f ( x ) = ( 0.625 ) 4 − 3 x − ( 1.6 ) x ( x + 8 )

The domain of f ( x ) = log 0.4 x − 1 x + 5 is

The range of f(x) = log { x } , where { } represents the fractional part function).

If f(x)= 4 – x 2 + x 2 – 1 , t h e n t h e m a x i m u m v a l u e o f ( f ( x ) ) 2 i s

Number of integral values of x satisfying the inequality 3 4 6 x + 10 − x 2 < 27 64 is

The domain of definition of the function y = 1 log 10 ( 1 − x ) – x + 2 is

The range of the function f ( x ) = e x − e | x | e x + e | x | is

If f ( x ) = 2 x 3 + 7 x − 5 , then f − 1 ( 4 ) is

Let R be the relation on the set of all real numbers defined by a R b iff | a − b | ≤ 1 . Then, R is

The range of the function, f ( x ) = cot − 1 log 0.5 x 4 − 2 x 2 + 3 i s

The domain of f ( x ) = 1 | cos x | + cos x is

If f : [ 0 , ∞ ) [ 0 , ∞ ) and f ( x ) = x 1 + x , then f is

f : N N , where f ( x ) = x − ( − 1 ) x . Then f is

If a function f : [ 2 , ∞ ) B defined by f ( x ) = x 2 − 4 x + 5 is a bijection, then B is equal to

Let f : R R , be defined as f ( x ) = e x 2 + cos x , then f is

Find the domain of the function f ( x ) = 2 x 2 − x + 1 − 1 x + 1 − 2 x − 1 x 3 + 1

The domain of f ( x ) = sin − 1 log 9 x 2 / 4 is

If A = {1, 2, 3, 4} and R = {(1, 1), (2, 2), (3, 3)} then the relation R on the set A is

f : R R f x 2 + x + 3 + 2 f x 2 − 3 x + 5 = 6 x 2 − 10 x + 17 ∀ x ∈ R then the value of f ( 100 ) is

If f x 2 − 6 x + 6 + f x 2 − 4 x + 4 = 2 x ∀ x ∈ R then f ( − 3 ) + f ( 9 ) − 5 f ( 1 ) =

g ( x ) is symmetrical about Let g ( x ) = f ( x ) − 1 . If f ( x ) + f ( 1 − x ) = 2 ∀ x ∈ R , then

which pair of functions is identical?

which of the following statements is incorrect

If f ( x ) = x 2 , for x ≥ 0 x , for x < 0 , then f o f ( x ) is given by

If e f ( x ) = 10 + x 10 − x , x ∈ ( − 10 , 10 ) and f ( x ) = k f 200 x 100 + x 2 then k =

Let f : ( − ∞ , 0 ] [ 1 , ∞ ) be defined as f ( x ) = ( 1 + − x ) − ( − x − x ) , then f ( x ) is

Which of the following functions is one-one?

Range of the function f ( x ) = log 2 2 − log 2 16 sin 2 x + 1 is :

The domain of the function f x = 1 C x – 1 10 – 3 × 10 C x is

The domain of f x = log 2 x + 3 x 2 + 3 x + 2 is

The domain of the function f x = log 10 5 x – x 2 4 1 / 2 is

The domain of the function f x = log 10 5 x – x 2 4 1 / 2 is

The domain of f x = cos – 1 2 – x 4 + log 3 – x – 1 is

The domain of the function f x = log 1 sin x

The domain of the function f x = l n x – 1 x 2 + 4 x + 4 is

The number of real solutions of the log 0 . 5 x = 2 x is

The domain of f x = 1 cos x + cos x is

If x is real, then the values of the expression x 2 + 14 x + 9 x 2 + 2 x + 3 are

The function f : R R is defined by f x = cos 2 x + sin 4 x or x ∈ R Then the range of f x is

The range of the function f x = x – 1 + x – 2 , – 1 ≤ x ≤ 3 is

The range of f x = sin – 1 x 2 + 1 x 2 + 2 is

The range of f x = sin x + cos x , where [.] denotes the greatest integer function, is

The range of the function, f x = e x – e x e x + e x

Let, P = x , y | x 2 + y 2 = 1 , x , y ∈ R . Then P is

For real numbers x and y, we write xRy ⇔ x – y + 2 is an irrational number. Then the relation R is

Let R be reflexive relation on a set A and I be the identity relation on A. Then

The relation R defined in N as aRb ⇔ b is divisible by a is

Let R be a relation on a set A such that R = R – 1 , then R is

Let R = { a , a } be a relation on a set A. Then R is

The relation “is subset of” on the power set P(A) of a set A is

The relation R defined on a set A is antisymmetric if ( a , b ) ∈ R ⇒ ( b , a ) ∈ R for

Let A be the non void set of the children in a family. The relation ‘x is a brother of y’ on A is

Let R 1 be a relation defined by R 1 = { a , b | a ≥ b , a , b ∈ R } . Then R 1 is

Which one of the following relations on R is an equivalence relation

If R is an equivalence relation on a set A, then R – 1 is

R is a relation over the set of real numbers and it is given by nm ≥ 0 . Then R is

The relation “congruence modulo m” is

Let S be the set of all real numbers. Then the relation R = a , b : 1 + ab > 0 on S is

Let R and S be two non-void relations on a set A. Which of the following statements is false

Let R be a relation on the set N be defined by x , y | x , y ∈ N , 2 x + y = 41 . Then R is

The number of symmetric relations defined on the set S = {a, b, c} is

If f : A B is a bijective function, then f – 1 o f is equal to

Let f : R R is a function defined by f ( x ) = 3 x – 4 , then f – 1 ( x ) is

If f (2x+3y, 2x-7y) =20x then f(x, y) equals

The domain of f(x) = log sin – 1 x 2 + x + 1 log ( x 2 – x + 1 ) is

If f : R R and F(x) = sin ( π { x } ) X 4 + 3 x 2 + 7 , Where { } is a fractional part of x , then

If n ( A ) = 4 , n ( B ) = 3 , n ( A × B × C ) = 24 , then n(C) is equal to

If A={1, 2, 3}, the number of reflexive relation in A is

The domain of the function f(x) = Cos -1 (sec (cos -1 X)) + sin -1 (Cosec(sin -1 X)) is

The domain of definition of function f ( x ) = log x 2 – 5 x – 24 – x – 2 , is

Let f : X Y , f ( x ) = sin x + cos x + 2 2 be invertible then X Y is /are.

If f ( x ) = sin 2 x and the composite functions g ( f ( x ) ) = | sin x | then g(x) is equal to

The domain of the function f ( x ) = sin − 1 log 2 1 2 x 2 is

The domain of the function f ( x ) = 1 x 12 − x 9 + x 4 − x + 1 is

The domain of the function f ( x ) = cos − 1 3 4 + 2 sin x is

The domain of the function f ( x ) = 1 − 1 − 1 − x 2 is

The domain of the function f ( x ) = log 2 log 2 log 2 … log 2 x ⏟ n times is

The domain of the function f ( x ) = log 3 − log 3 x 2 + 5 log 3 x − 6 is

The domain of the function f ( x ) = log 3 − log 3 x 2 + 5 log 3 x − 6 is

The range of the function y = sin − 1 x 2 1 + x 2 is

The range of the function y = e − x 1 + [ x ] is

The inverse of the function f ( x ) = a x − a − x a x + a − x is

The function f ( x ) = sec log x + 1 + x 2 is

A function whose graph is symmetrical about the origin is given by

The period of the function f ( x ) = sin x is

The value of n ∈ I for which the function f ( x ) = sin nx sin x n has 4 π as its period is

π is the period of the function

If f (x + y, x – y) = xy, then the arithmetic mean of f (x, y) and f ( y, x) is

Let f(x) = (x + 1) 2 – 1, x ≥ –1 then the set {x : f(x) = f –1 (x)} is equal to

Let R be a relation on R defined as a R b if a ≤ b . Then, relation R is

The relation R defined by ‘ > ‘ on the set N is

The domain of the function f ( x ) = sin – 1 x – 3 9 – x 2

The relation a R b defined by a is factor of b on N is not

The domain of y = cos – 1 ( 1 – 2 x ) is

Let X = {1, 2, 3, 4}. The number of equivalence relations that can be defined on X is

The function f ( x ) = x 2 log 1 – x 1 + x is

The domain of y = cos – 1 1 – 2 x 4 is

Which of the following functions is bounded

Let I be the set of integers. For a , b ∈ I , a R b if and only if | a – b | < 1 , then

The range of the function f ( x ) = 7 − x P x − 3 is

Let R = { ( x , y ) : x , y ∈ A , x + y = 5 } where A = { 1 , 2 , 3 , 4 , 5 } then

The domain of definition of the functions y ( x ) given by the equation a x + a y = a ( a > 1 ) is

If 2 f x 2 + 3 f 1 x 2 = x 2 − 1 , then f ( x 2 ) is

If n ( A ) = 3 and n ( B ) = 5 then number of one-one functions that can be defined from A to B is

If the function f : [ 1 , ∞ ) [ 1 , ∞ ) is defined by f ( x ) = 2 x ( x − 1 ) then f − 1 ( x ) is

Let x , y ∈ I and suppose that a relation R on I is defined by x R y if and only if x ≤ y then

If f : R R given by f ( x ) = a x + sin x + a , then f is one-one and onto for all

The period of the function f ( x ) = cos 2 3 x + tan 4 x is

Let f : ( 1 , ∞ ) ( 1 , ∞ ) be defined by f ( x ) = x + 2 x − 1 . Then

Given f ( x ) = 1 | x | − x and g ( x ) = 1 x − | x | then

If f ( x + y ) = f ( x y ) ∀ x , y ε R , and f ( 2013 ) = 2013, then f(– 2013) equals