Question

What is the inverse of f(x)=2(3^x)

Answer 1

If
`f^(-1)(x)` is the inverse of
`f(x)`, then by definition

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

so that

`2 * 3^{f^(-1)(x)} = x`

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

`3^{f^(-1)(x)} = \frac x2`

`\log_3\left(3^{f^(-1)(x)}\right) = \log_3\left(\frac x2\right)`

`f^(-1)(x) \log_3(3) = \log_3\left(\frac x2\right)`

`\boxed{f^(-1)(x) = \log_3\left(\frac x2\right)}`