JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

1 of 1

Analyzing +4 | -1

f(x)+2 f\left(\frac{1}{x}\right)=3 x, x \neq 0

and

{S}=\{{x} \in {R}: {f}({x})={f}(-{x})\}

; then

{S}

View answer and explanation

Correct option: A

Contains exactly two elements.

Option A (Contains exactly two elements) is correct because solving the functional equation leads to f(x) = 2/x - x, and f(x) = f(-x) gives two solutions: x =

\sqrt{2}

and x = -

\sqrt{2}

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