Question

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

Answer 1

If $f^{-1}(x)$ is the inverse of

$f(x) = \dfrac23x+9$

then

$f\left(f^{-1}(x)\right) = \dfrac23f^{-1}(x) + 9 = x$

Solve for $f^{-1}(x)$ :

$\dfrac23f^{-1}(x)+9 = x \\\\ \dfrac23f^{-1}(x) = x-9 \\\\ f^{-1}(x) = \dfrac32(x-9) = \dfrac32x-\dfrac{27}2$

which makes D the correct answer.