What does the notation $\min_x$ mean?

Question

I have a problem in which I need to find $\min_x(f(x))$. What does this notation mean?

Answer 1

In the contexts I've seen, $\min_x(f(x))$ , means "the minimum of $f(x)$ over all $x$".

Answer 2

It means the minimum of the function $f$ when $x$ is varying over the domain of $f$.

Answer 3

$\min_{x\in A}f(x)$ it's just another way to write $\min\{f(x):x\in A\}$