Answer:
[tex]f^{-1}[/tex](x) = [tex]\frac{1}{3}[/tex] x + 7
Step-by-step explanation:
let y = f(x) and rearrange making x the subject, that is
y = 3(x - 9) + 6 ← distribute and simplify right side
y = 3x - 27 + 6 = 3x - 21 ( add 21 to both sides )
y + 21 = 3x ( divide all terms by 3 )
[tex]\frac{1}{3}[/tex] y + 7 = x
Change y back into terms of x with x = [tex]f^{-1}[/tex](x) , thus
[tex]f^{-1}[/tex](x) = [tex]\frac{1}{3}[/tex] x + 7
