If [tex]f^{-1}(x)[/tex] is the inverse of [tex]f(x)[/tex], then
[tex]f\left(f^{-1}(x)\right) = x[/tex]
Given
[tex]f(x) = 3x-9[/tex]
composing with the inverse function gives
[tex]f\left(f^{-1}(x)\right) = 3f^{-1}(x) - 9 = x[/tex]
Solve for the inverse:
[tex]3f^{-1}(x)-9 = x \\\\ 3f^{-1}(x) = x+9 \\\\ \boxed{f^{-1}(x) = \dfrac x3 + 3}[/tex]
