Question

If $g$ is the inverse of a function $f$ and $f^{\prime }\left(x\right)=\frac{1}{1+x^5},$ then $g^{\prime }(x)$ is equal to :

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

Answer 1

Answer: (B)

$f^{\prime }(x)=\frac{1}{1+x^5}=f(g(x))=x\to f^{\prime }(g(x))g^{\prime }(x)=1$
$g^{\prime }(x)=\frac{1}{f^{\prime }(g(x))}=1+(g(x){)}^5$