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

If $f(x)$ and $g(x)$ are inverse functions of each other and $f(x) = x + e^x$, then $g'(x) = ...$

State with reason whether the following function has an inverse: $g : \{5, 6, 7, 8\} \rightarrow \{1, 2, 3, 4\}$ with $g = \{(5, 4), (6, 3), (7, 4), (8, 2)\}$.

$A$ condition for a function $y = f(x)$ to have an inverse is that it should be

Suppose $f(x)=(x+1)^{2}$ for $x \geq -1$. If $g(x)$ is a function whose graph is the reflection of the graph of $f(x)$ in the line $y=x$,then $g(x) = $

The inverse of the function $f(x) = \frac{e^x - e^{-x}}{e^x + e^{-x}} + 2$ is given by