What is the inverse of f(x) = x2 − 9?

To  make this easier to type, I'm going to replace f(x) with y, to give the equation:

    y  =  x² - 9

To find the inverse, use this two-step process:

Step 1:  interchange x and y:

    x  =  y² - 9

Step 2:  solve for y:

   x + 9  =  y²

    y²  =  x + 9

    y  =  ±√(x + 9)

In theis case, the inverse is not a function.