If $f: R \rightarrow R$ is defined by $f(x)=x^{3}$,then $f^{-1}(8)$ is equal to

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

Let $e^{f(x)} = \ln x$. If $g(x)$ is the inverse function of $f(x)$,then $g'(x)$ is equal to:

If the functions $f$ and $g$ are defined by $f(x) = 3x - 4$ and $g(x) = 2 + 3x$ for $x \in R$,then $g^{-1}(f^{-1}(5))$ is equal to

Let $f : R \to R$ be defined by $f(x) = \ln(x + \sqrt{x^2 + 1})$. Then the number of solutions of $|f^{-1}(x)| = e^{-|x|}$ is

If $f(x) = (x + 1)^2$ for $x \ge 1$, and $g(x)$ is a function whose graph is the reflection of the graph of $f(x)$ in the line $y = x$, then $g(x)$ is: