The inverse of a function is when you switch the variables and solve for y again. For example, you function
[tex]y = \sqrt{2x - 3} + 2[/tex]
[tex]x = \sqrt{2y - 3} + 2[/tex]
Now solve for y
[tex] \sqrt{2y - 3} = x - 2[/tex]
[tex]2y - 3 = ({x - 2})^{2} [/tex]
[tex]2y = {(x - 2)}^{2} + 3[/tex]
[tex]y = \frac{{(x - 2)}^{2} + 3}{2}[/tex]
