Please help!
What is the inverse of f(x)=x2 - 11 if the domain is x > 0

Inverse means to reflect the graph on the plane of y=x
Thus simply switch x with y and isolate y,
x = y2 - 11
y2 = x + 11
y = root (x + 11)

The inverse of f(x) is:

y = root (x + 11)
range is y is greater than 0