Question

If $g$ be an inverse function of $f$ and $f^{\prime }\left(x\right)=\frac{1}{1+x^5}$, then $g^{\prime }\left(x\right)$ will be

• A. $1+x^5$
• B. $1+{\left\{g\right(x\left)\right\}}^5$
• C. $\frac{1}{1+{\left\{g\right(x\left)\right\}}^5}$
• D. $5x^4$

Answer 1

The correct option is B $1+{\left\{g\right(x\left)\right\}}^5$

$g$ is inverse of function F, then

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

Differentiating $wrtn$

$f^1\left(g\left(n\right)\right)\ast g^1\left(n\right)=1$

$g^1\left(n\right)=\frac{1}{f^1\left(g\left(n\right)\right)}=1+{\left(g\left(n\right)\right)}^5$