Question

What is the domain of `y=3/2 arcsin(2x+.5)`?

Answer 1

`-3/4 <= x <= 1/4`

Explanation:

The domain of `sin^-1(u)` is `-1<=u<=1`, so for this problem we need to solve:

`-1<=2x+1/2<=1`

subtracting `1/2` from all parts:

`-3/2 <= 2x <= 1/2`

dividing through by 2:

`-3/4 <= x <= 1/4`