Question

F(x)=-3/4x+9 what are the steps for finding f^-1(x)

Answer 1

The inverse function
`f^(-1)(x)` is such that

`f\left(f^(-1)(x)\right) = x`

If
`f(x)=-\frac34x+9`, then we have

`f\left(f^(-1)(x)\right) = -\frac34f^(-1)(x)+9 = x`

Solve for the inverse :

`-\frac34f^(-1)(x)+9 = x \\\\ -\frac34f^(-1)(x) = x-9 \\\\ f^(-1)(x) = -\frac43(x-9) \\\\ \boxed{f^(-1)(x) = -\frac43x+12}`