Answer:
[tex]f^{-1}(x)=x^2+3[/tex]
Step-by-step explanation:
We begin with the function [tex]f(x)=(x-3)^{\frac{1}{2} }[/tex]
The first thing we must do is swap the locations of f(x) and x. For the sake of simplicity, lets replace f(x) with y.
[tex]x=(y-3)^{\frac{1}{2} }[/tex]
Now, we just need to solve for y
[tex]x=(y-3)^{\frac{1}{2} } \\\\x^{2} =y-3\\\\y=x^2+3\\\\f^{-1}(x)=x^2+3[/tex]
