Let $f(x)=x^5+2 \mathrm{e}^{x / 4}$ for all $x \in \mathbf{R}$. Consider a function $g(x)$ such that $(g \circ f)(x)=x$ for all $x \in \mathbf{R}$. Then the value of $8 g^{\prime}(2)$ is :

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Aicharya · Accepted Answer

$\begin{aligned} & f(x)=2 \ & 	ext { when } x=0 \ & \because g^{\prime}(f(x)) f^{\prime}(x)=1 \ & g^{\prime}(2)=\frac{1}{f^{\prime}(0)} \ & \because f^{\prime}(x)=5 x^4+\frac{2}{4} e^{x / 4} \ & g^{\prime}(2)=2 \ & 	ext { Ans }=16 \ & 	ext { Option (1) }\end{aligned}$

Let $f(x)=x^5+2 \mathrm{e}^{x / 4}$ for all $x \in \mathbf{R}$. Consider a function $g(x)$ such that $(g…

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