Question

If f(x) = 2/3x + 9, find f^-1(x)

Answer 1

If
`f^(-1)(x)` is the inverse of

`f(x) = \frac23x+9`

then

`f\left(f^(-1)(x)\right) = \frac23f^(-1)(x) + 9 = x`

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

`\frac23f^(-1)(x)+9 = x \\\\ \frac23f^(-1)(x) = x-9 \\\\ f^(-1)(x) = \frac32(x-9) = \frac32x-\frac{27}2`

which makes D the correct answer.