To solve this problem you must apply the proccedure shown below:
You must switch the variables, and then, you must solve for [tex] y [/tex], as following:
[tex] x=-\frac{1}{2} \sqrt{y} +3\\ (x-3)^{2} = (\frac{1}{2}\sqrt{y})^{2} \\ y=4x^{2} -24x+36\\ f^{-1} (x)=4x^{2} -24x+36 [/tex]
Therefore, as you can see, the answer is: [tex] f^{-1} (x)= 4x^{2} -24x+36
[/tex]
