If f(x) and g(x) are continuous functions and fog is an identity function such that g'(b) = 5, and g(b) =a, then f'(a) is :
Answer & explanation
Correct answer: option 2
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 $x=b$
$f'(g(b))=\frac{1}{g'(b)}$
$f'(a)=\frac{1}{5}$