Answer:
[tex]f^{-1} (x)=\frac{x}{3}+3[/tex]
Step-by-step explanation:
write as an equation
[tex]y=3x-9[/tex]
interchange the variables
[tex]x=3y-9[/tex]
solve for y:
[tex]3y-9=x[/tex]
add 9 to both sides
[tex]3y=x+9[/tex]
divide each term by 3
[tex]\frac{3y}{3} =\frac{x}{3}+\frac{9}{3}[/tex]
simplify
[tex]y=\frac{x}{3}+3[/tex]
replace y with [tex]f^{-1}(x)[/tex] to show the final answer of the inverse
[tex]f^{-1} (x)=\frac{x}{3}+3[/tex]
