Question

Let $f:R\to R$ be a function defined as $f(x)=x^3+x-1$ and $g$ is inverse of $f$, then the value of $\frac{g(9)}{g^{\prime }(9)}$ is equal to

• A. 10
• B. 15
• C. 20
• D. 26

Answer 1

Answer: (D)

$\because g^{\prime }(f(x))=\frac{1}{f^{\prime }(x)}$
Here $f(x)=9$, when $x=2$
$\therefore g^{\prime }(9)=\frac{1}{f^{\prime }(2)}$
Clearly $f^{\prime }(x)=3x^2+1\Rightarrow f^{\prime }(2)=13$

$\therefore g^{\prime }(9)=\frac{1}{13}$
$\because f(2)=9\Rightarrow f^{-1}(9)=g(9)=2$
$\therefore \frac{g(9)}{g^{\prime }(9)}=26$