If $f: R \rightarrow R$ is a mapping defined by $f(x)=x^{3}+5$,then $f^{-1}(x)$ is equal to

Let $g$ be the inverse function of $f$ and $f'(x) = \frac{x^{10}}{1 + x^2}$. If $g(2) = a$,then $g'(2)$ is equal to:

If the function $f(x) = x^5 + e^{x/5}$ and $g(x) = f^{-1}(x)$,then the value of $\frac{1}{g'(1 + e^{1/5})}$ is

Which of the following functions is the inverse of itself?

The inverse of the function $y = \frac{10^x - 10^{-x}}{10^x + 10^{-x}}$ is

Let $f: R - \{3\} \rightarrow R - \{1\}$ be defined by $f(x) = \frac{x-2}{x-3}$. Let $g: R \rightarrow R$ be given as $g(x) = 2x - 3$. Then,the sum of all the values of $x$ for which $f^{-1}(x) + g^{-1}(x) = \frac{13}{2}$ is equal to ...... .