If f(x) and g(x) are continuous functions and log is an identity function such that g'(b) = 5, and g(b) =a, then f'(a) is :

$\frac{1}{5}$

The correct answer is Option (2) → $\frac{1}{5}$

$g'(b) = 5$, $g(b) =a$, $f(a)=?$

fog is an identity function 

$⇒f^{-1}(x)=g(x)$

$$f(g(x))=x,g(f(x))=x$

differentiating $fog(x)$

we get $f'(g(x))g'(x)=1$

$f'(g(x))=\frac{1}{g'(x)}$

at $x=b$

$f'(g(b))=\frac{1}{g'(b)}$

$f'(a)=\frac{1}{5}$