Question

Let $g\left(x\right)$ be the inverse of an invertible function $f\left(x\right)$ which is differentiable at $x=c$, then $g^{\prime }\left(f\right(c\left)\right)$ equals

• A. $f^{\prime }\left(c\right)$
• B. $\frac{1}{f^{\prime }\left(c\right)}$
• C. $f\left(c\right)$
• D. $Noneofthese$

Answer 1

The correct option is B $\frac{1}{f^{\prime }\left(c\right)}$

Given,

$g\left(f\right(c\left)\right)=c$

$g^{\prime }\left(f\right(c\left)\right).f^{\prime }\left(c\right)=1$

$\Rightarrow g^{\prime }\left(f\right(c\left)\right)=\frac{1}{f^{\prime }\left(c\right)}$