The inverse of a function is what reverses it. That is, if a function outputs y for an input x, then its inverse will output x for an input y.
To find the inverse of a function, we interchange x and y in the equation.
Here, we have [tex](x-4)^2- \frac{2}{3} = 6y-12[/tex].
We first interchange x and y.
[tex](y-4)^2- \frac{2}{3} = 6x-12[/tex]
This form is technically an inverse already, but by convention and for the answer choices, we will now solve for y.
[tex](y-4)^2= 6x-12+\frac{2}{3} \\ \\ (y-4)^2 = 6x- \frac{34}{3} \\ \\ y-4= \sqrt{6x-\frac{34}{3}} \\ \\ y = 4\pm\sqrt{6x-\frac{34}{3}}[/tex]
