Because f(x) is not a 1 to 1 mapping the inverse doesn't exist unless you restrict the domain of x.
if you restrict x to {x:x >= 7} you could find
y=x2+7
y−7=x2
x=√y−7
f−1(x)=√x−7
on the other hand if you restrict x to {x: x <= -7} you get
f−1(x)=√7−x
