The inverse of a function is calculated solving the function for x.
So, we have the function:
[tex]f(x)=3x-7[/tex]Let's replace f(x) by y and solve for x, as:
[tex]\begin{gathered} y=3x-7 \\ y+7=3x-7+7 \\ y+7=3x \\ \frac{y+7}{3}=\frac{3x}{3} \\ \frac{y}{3}+\frac{7}{3}=x \end{gathered}[/tex]So, to calculate the inverse function we need to change y and x as:
[tex]y=\frac{x}{3}+\frac{7}{3}[/tex]