The inverse of cos x is a function. the domain of cos x could be? PLEASE HELP

answer choices

x:-2π ≤ x ≤ 0
x:-π ≤ x ≤ π
x: 0 ≤ x ≤ 2π
x: 0 ≤ x ≤ π

can you please explain why ? thank you so much !!

In order for the inverse of cos(x) to be a function, the domain of cos(x) needs to be restricted in such a way that cos(x) is either monotonically increasing or decreasing throughout the restricted domain.

The only answer choice that reflects this is (b) -π ≤ x ≤ π.

I hope this helps!