JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

1 of 1

Analyzing +4 | -1

If the function

f: \mathbb{R} \rightarrow \mathbb{R}

satisfies the relation

f(x)+

f(x+4)=f(x+2)+f(x+6)

for all

x \in \mathbb{R}

, then a period of

f

View answer and explanation

Correct option: D

The correct answer is D (8) because the given relation implies that the function has a period of 8, derived by substituting

x-2

into the original equation and comparing.

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

f(x)=x(4-x)

f^{-1}(x)

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

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

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

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

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

f: R \rightarrow R

f(x)=x^4

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

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