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Q.

Statement–I: The range of function $f (x) = sgn (x^{2} - 2 x + 3)$ is ${1}$
Statement–II: The range of function $f (x) = [\sin {x}]$ is ${0}$ where ${.}$ represents the fractional part of function and $[.]$ represents the greatest integer function

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a

Both S-I & S–II are true and S–II is correct explanation of S-I

b

Both S-I & S–II are true and S–II is NOT correct explanation of S-I

c

S–I is true and S–II is false

d

S–I is false and S–II is true

answer is B.

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Detailed Solution

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$I \to f (x) = sgn ({(x - 1)}^{2} + 1) = 1 {∵ {(x - 1)}^{2} + 1 > 0, \forall x \in R}$

$I I \to f (x) = [\sin {x}]$

Since $0 \leq {x} < 1 \Rightarrow 0 \leq \sin {x} < \sin 1 \Rightarrow [\sin {x}] = 0$

Range is ${0}$

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Statement–I: The range of function f(x)=sgn(x2−2x+3) is {1}Statement–II: The range of function f(x)=[sin{x}] is {0} where {.} represents the fractional part of function and [.] represents the greatest integer function