Question

What is the domain and range of `y =arccos(sin(2x))`?

Answer 1

The domain is `RR` and the range is `[0,pi]`

Explanation:

The domain of the function `arccos y` is the interval `[-1,1]`.

As `-1<=sin(2x) <=1 AA x in RR`

The function `arccos(sin(2x))` is defined for every `x`.

Besides, `sin(2x)` assumes every possible value in the domain of `arccos y` so the range of the function is the same as the natural range of `arccos`, that is the interval `[0,pi]`.