Question

Let f(x) = x2 - 81. Find f-1(x).

Answer 1

To make this simpler, make f(x) be y.

`f(x)= x^(2) -81\\ y=x^(2) -81\\`

Switch x and y to find inverse

`y=x^(2) -81\\ x=y^(2) -81\\`

Now, solve for y.

`x=y^(2) -81\\ x+81=y^(2) -81+81\\ x+81=y^(2)\\ √(x+81) = \sqrt{y^(2)} \\ y =√(x+81)`