f(x) = (x-4)^{1/2}
y = (x-4)^{1/2}
Switch the x's and y's, solve for the new y:
x = (y-4)^{1/2}
x^{2} = y-4 [Square both sides to get rid of the square root]
x^{2}+4 = y = f^{-1}(x)
Check:
f(f^{-1}(x)) = (f^{-1}(x)-4)^{1/2} = (x^{2}+4-4)^{1/2} = (x^{2})^{1/2} = x Check!