Q.
Which of the following functions is an injective (one-one) function in its respective domain?
see full answer
Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!
Real Strategies. Real People. Real Success Stories - Just 1 call away
An Intiative by Sri Chaitanya
a
f(x)=2x+sin3x
b
f(x)=x⋅[x], (where [.] denotes the G.I.F)
c
f(x)=2x−14x+1
d
fx =2x+14x-1
answer is D.
(Unlock A.I Detailed Solution for FREE)
Ready to Test Your Skills?
Check your Performance Today with our Free Mock Test used by Toppers!
Take Free Test
Detailed Solution
1 If fx=2x +sin3x ⇒ f'x =2 +3 cos3x =0 ⇒ cos 3x=-23 ,which is defined and f''x =- 9 sin3x = -35<0 so fx has maximum value exists in its domain , so it is not one-one2 fx = x.x is not one-one since f0.1=0.1 ×0 =0 and f0.2=0 3 fx=2x-14x+1 ⇒ fx is continuous function and f0=0 and fx →0 again when x→∞ since y =12x-14x1+14x →0 as x→∞ hence fx has a atleat one maximum exists , so it is not one-one4 fx =2x+14x-1 =2x+12x-12x+1 =12x-1 ⇒ f'x = -2x log22x-12<0 ⇒fx is decreasing function so it is one-one