let's recall that for any expression, its inverse will have its domain as its range and its range as its domain, now that sounds like a mouthful.
Another way to say it is, if the original function has a domain ⅅ and a range ℝ, then its inverse will have a domain of ℝ and a range of ⅅ, so the inverse (x , y) pairs are pretty much the same as the original but flipped sideways, for example on the function above we have a point at (π , -0.5), so the inverse function will have a point of (-0.5 , π) pretty much the same thing but flipped sideways. What the hell all that means?
well, if we look above, the ℝange goes up to 0.5 and down to -0.5, so that means the ⅅomain of the inverse is just that, from 0.5 down to -0.5.
-0.5 ⩽ x ⩽ 0.5.