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

State with reason whether following functions have inverse $f: \{1,2,3,4\}\rightarrow\{10\}$ with $f =\{(1,10),(2,10),(3,10),(4,10)\}$

If $f(x) = \frac{x}{{1 + x}}$, then ${f^{ – 1}}(x)$ is equal to

The inverse of the function $\frac{{{{10}^x} – {{10}^{ – x}}}}{{{{10}^x} + {{10}^{ – x}}}}$ is

Let $Y =\left\{n^{2}: n \in N \right\} \subset N .$ Consider $f: N \rightarrow Y$ as $f(n)=n^{2}$  Show that $f$ is invertible. Find the inverse of $f$