Question

Find the domain and range of ${\tanh }^{-1}x$ by plotting the graph.

Answer 1

$y={\tanh }^{-1}x=\frac{1}{2}\ln \left(\frac{1-x}{1+x}\right)$

The above graph is the graph of ${\tanh }^{-1}x$

$\therefore$ Domain and range of ${\tanh }^{-1}x$ is

$y\in (-\infty ,\infty )$ and, $x\in (-1,1)$ as, $x$ can never be equal to zero.