JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f(\mathrm{x})=\mathrm{x}^5+2 \mathrm{e}^{\mathrm{x} / 4}\) for all \(\mathrm{x} \in \mathrm{R}\). Consider a function \(g(x)\) such that \((gof) (x)=x\) for all \(x \in R\). Then the value of \(8 g^{\prime}(2)\) is :
- A \(16\)
- B \(4\)
- C \(8\)
- D \(2\)
Answer & Solution
Correct Answer
(A) \(16\)
Step-by-step Solution
Detailed explanation
\( f(x)=2 \) when \( x=0 \) \( \because g^{\prime}(f(x)) f^{\prime}(x)=1 \) \( g^{\prime}(2)=\frac{1}{f^{\prime}(0)} \) \( \because f^{\prime}(x)=5 x^4+\frac{2}{4} e^{x / 4} \) \( g^{\prime}(2)=2 \) Ans \(=16 \) Option (\(1\))
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