JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

1 of 1

Application +4 | -1

Let

f(x)=x^5+2 e^{x/4}

for all

x \in R

. Consider a function

g(x)

such that

(gof)(x)=x

for all

x \in R

. Then the value of

8 {g}^{\prime}(2)

is:

View answer and explanation

Correct option: A

Option A (16) is correct because it is derived from finding the derivative of the inverse function and evaluating at the given point.

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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\}