Question

Let $f(x)>0$ for all $x$ and $f^{\prime}(x)$ exists for all $x$. If $f$ is the inverse function of $h$ and $h^{\prime}(x)=\frac{1}{1+\log x} .$ Then $f^{\prime}(x)$ will be
(A) $1+\log (f(x))$
(B) $1+f(x)$
(C) $1-\log (f(x))$
(D) $\log f(x)$

Answer 1

Ans: (A)
Hint $: h(f(x))=x \Rightarrow h^{\prime}(f(x)) \cdot f^{\prime}(x)=1 \Rightarrow f^{\prime}(x)=\frac{1}{h^{\prime}(f(x))} \Rightarrow f^{\prime}(x)=1+\log (f(x))$

Answer 2

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Answer 3

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