Solution:
Given the function:
[tex]f(x)=3x+12[/tex]To find the inverse,
step 1: Let y represent f(x).
Thus,
[tex]\begin{gathered} f(x_)=3x+12 \\ where\text{ y=f\lparen x\rparen} \\ \Rightarrow y=3x+12 \end{gathered}[/tex]step 2: Swap the position of y for x.
Thus,
[tex]x=3y+12[/tex]step 3: Make y the subject of the equation in step 2.
Thus,
[tex]\begin{gathered} x=3y+12 \\ subtract\text{ 12 from both sides of the equation,} \\ x-12=3y+12-12 \\ \Rightarrow x-12=3y \\ divide\text{ both sides by the coefficient of y, which is 3} \\ \frac{x-12}{3}=\frac{3y}{3} \\ \frac{x}{3}-\frac{12}{3}=y \\ \Rightarrow y=\frac{1}{3}x-4 \end{gathered}[/tex]Thus, the inverse of the function is
[tex]f^{-1}(x)=\frac{1}{3}x-4[/tex]The graphs of the function and its inverse are as shown below:
