ANSWER
[tex]f^{-1}(x)\text{ = }\frac{x}{3}\text{ - 4}[/tex]EXPLANATION
We want to find the inverse of:
f(x) = 3x + 12
To do this, first replace f(x) with y:
=> y = 3x + 12
Now, make x the subject of the formula:
y - 12 = 3x
[tex]\begin{gathered} \Rightarrow\text{ x = }\frac{y}{3}\text{ - }\frac{12}{3} \\ x\text{ = }\frac{y}{3}\text{ - 4} \end{gathered}[/tex]Now, replace the x with f-1(x) and replace the y with x:
[tex]f^{-1}(x)\text{ = }\frac{x}{3}\text{ - 4}[/tex]