The thing that might prevent from having an inverse is if there are two distinct values of for which the values of are the same. This can happen with things like because and (for example) both give .
So with an expression like you need to look at the value of that makes , because either side of that, you'll have two values of giving the same value of . Clearly that value is . So when (for example) and , the value of is the same: it's in each case.
For part (i) we are told that lies in the range . So we are certainly allowed some values of that are less than . Therefore if is going to have an inverse, we must avoid any values of x that are greater than in order to avoid repeating the values of . Hence (the greatest permitted value of ) .
For part (ii) we know that has an inverse. So we know that , and hence . So to find we must be changing the sign of from negative to positive. In other words, when .