Your answer is √(x + 4).
A strange way to find the inverse of a function is to write it first as y = x² - 4, and then to switch the y and x around to get x = y² - 4. Then you just solve for y, so:
x = y² - 4
+ 4
x + 4 = y²
√
√(x + 4) = y
I hope this helps!