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

If $f$ be the greatest integer function and $g$ be the modulus function, then $(gof)\left( { - \frac{5}{3}} \right) - (fog)\left( { - \frac{5}{3}} \right) = $

Let $f: X \rightarrow Y$ be an invertible function. Show that the inverse of $f^{-1}$ is $f$, i.e., $\left(f^{-1}\right)^{-1}=f$.

Which of the following function is inverse function

The relation $R$ is defined on the set of natural numbers as $\{(a, b) : a = 2b\}$. Then $\{R^{ - 1}\}$ is given by

If $X$ and $Y$ are two non- empty sets where $f:X \to Y$ is function is defined such that $f(c) = \left\{ {f(x):x \in C} \right\}$ for $C \subseteq X$ and ${f^{ - 1}}(D) = \{ x:f(x) \in D\} $ for $D \subseteq Y$ for any $A \subseteq X$ and $B \subseteq Y,$ then