Question

If $f(x)=x^3+\ln x+1$ and $g(x)$ is the inverse function of $f(x)$ then ${\left(g^{\prime }(2)\right)}^{-1}$ is equal to

• A. 11
• B. 10
• C. 8
• D. 4

Answer 1

Answer: (D)

$f(x)=x^3+\ln x+1\Rightarrow f^{\prime }(x)=3x^2+\frac{1}{x}$
$f(1)=2$
$g^{\prime }(2)=\frac{1}{f^{\prime }(1)}=\frac{1}{4}\Rightarrow {\left(g^{\prime }(2)\right)}^{-1}=4$