The hyperbolic sine $\mathbb R\to\mathbb R,~x\to\sinh(x)$ is invertible for all real numbers $x\in\mathbb R.$ Its inverse function is called the inverse hyperbolic sine $$\operatorname{arsinh}:\mathbb R\to\mathbb R,$$ and can be calculated using the formula $$\operatorname{arsinh}(x)=\ln\left(x+\sqrt{1+x^2}\right).$$
The following graph visualizes the inverse hyperbolic sine function:
Proofs: 1
