[Math] What does $\exp(f)$ mean

Question

In several posts around this site, I have encountered the expression $\exp(x)$ where $x$ is an arbitrary expression. What does this notation mean?

Answer 1

$\exp(x) = e^x{}{}{}{}{}{}{}{}{}{}{}{}{}$

It's often used when we have $\exp(f(x)) = e^{f(x)}$ and $f(x)$ is complicated function. The focus, then, becomes the function in the exponent of $e$ (not to mention that it helps readers to not have to squint to read, say when $f$ is a rational function, $e^{f(x)}$).