Question

Let $f$ and $g$ be differentiable function satisfying $g^{\prime }\left(a\right)=2,g\left(a\right)=b$ and $g=f^{-1}$,

then $f^{\prime }\left(b\right)$ is equal to?

• A. $\frac{1}{2}$
• B. $2$
• C. $\frac{2}{3}$
• D. $3$

Answer 1

The correct option is A $\frac{1}{2}$

$\left(fog\right)\left(x\right)=x$
$\frac{d}{dx}\left(fog\right(x\left)\right)=1$
$f^{\prime }\left(g\right(x\left)\right)g^{\prime }\left(x\right)=1$
Put $x=a$
$f^{\prime }\left(b\right)g^{\prime }\left(a\right)=1$

$f^{\prime }\left(b\right)=\frac{1}{2}$