Find the inverse of `f(x)=3sqrt(x+3)` :
The typical way to find the inverse is to exchange x and y and solve for y:
But there is a problem. The original function had a domain restriction; `x>=-3` . We must take this into account. The range of the original function was `y>=0` so the domain of the inverse is `x>=0` .
If `f(x)=3sqrt(x+3)` then the inverse `f^(-1)(x)=1/9x^2-3,x>=0`
The graph of the function (green) and the inverse (red):
Note that as expected the graphs are reflections across the line y=x.