Question

Please help, need to find f^-1 (x)

Answer 1

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

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

Plugging
`f^(-1)(x)` into
`f(x)` gives us

`f\left(f^(-1)(x)\right) = (3f^(-1)(x) + 3)/(5f^(-1)(x) + 6) = x`

Solve for
`f^(-1)(x)` :

`(3f^(-1)(x) + 3)/(5f^(-1)(x) + 6) = x \\\\ 3f^(-1)(x)+3=x\left(5f^(-1)(x)+6\right) \\\\ 3f^(-1)(x) + 3 = 5x f^(-1)(x)+6x \\\\ 5xf^(-1)(x)-3f^(-1)(x) = 3 - 6x \\\\ (5x-3)f^(-1)(x)=3-6x \\\\ \boxed{f^(-1)(x)=(3-6x)/(5x-3)}`