The real hyperbolic cosine function is a function defined using the real exponential function by the formula
\[\cosh(x):=\frac 12(\exp(x)+\exp(-x))\]
for all \(x\in\mathbb R\). Note that $\cosh$ can be interpreted as the "average" of $\exp(x)$ and $\exp(-x)$.
The following graph visualizes the hyperbolic cosine function: