Question

What is the domain and range of `f(x)=sqrt[Cos[x]]`?

Answer 1

Domain:
`[-pi/2+2pi n,pi/2+2pi n]` for all integer `n`

Range:
`[0,1]`

Explanation:

If author used square brackets inside `cos` just as brackets (not as an absolute value, which it looks like in a small font), than here is the explanation.

Also it should be noted that the square root in this problem used without `+-` sign implies arithmetic square root, that is only its non-negative value.

Square root requires `cos x` to be non-negative, which entails that `x` must be in the intervals `[-pi/2+2pi n,pi/2+2pi n]` for all integer `n`. That assures non-negativity of `cos x` and, therefore, constitutes the domain of this function.

In this domain `cos x` ranges in the interval `[0,1]` and square root of it also will be in the same range.