JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

1 of 1

Application +4 | -1

Let

f(x)=\frac{x \cdot e^x}{e^x-1}.

f(x)

can be written as sum of an even function,

g(x)

and an odd function,

h(x)

then the value of

h(4)

View answer and explanation

Correct option: A

Option A (2) is correct because the odd function h(x) is found to be x/2, and h(4) = 4/2 = 2.

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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\}