JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

1 of 1

Analyzing +4 | -1

f: R \rightarrow R, f(x)=\left\{\begin{array}{cc}x|x|-4, & x \in Q \\ x|x|-\sqrt{3} & x \in Q\end{array}\right.

, then

f(x)

View answer and explanation

Correct option: D

many to one and into

Option B (many to one and onto) is incorrect. The correct answer is many to one and into because f(2) = f(3^(1/4)) indicating many-to-one, and f(x) ≠ -√3 for all x ∈ R, indicating into.

More Questions from FUNCTIONS

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f:(-\infty, 2] \longrightarrow(-\infty, 4]

, where

f(x)=x(4-x)

, then

f^{-1}(x)

is given by: If

g(f(x))=|\sin x|

and

f(g(x))=(\sin \sqrt{x})^2

, then Let

f:\left( {2,\;3} \right) \to \left( {0,\;1} \right)

be defined by

f\left( x \right) = x - \left[ x \right]

, then

{f^{ - 1}}\left( x \right)

equals Let

f: R \rightarrow R

be defined as

f(x)=x^4

, Choose the correct answer. Which of the following functions are odd functions Let

f(x)=(x+1)^2-1(x \geq-1)

. Then the set

S=\left\{x: f(x)=f^{-1}(x)\right\}

contains