To determine the inverse of the function we need to follow these steps:
1 - Replace f(x) by y;
2 - Switch the places of x and y on the expression;
3 - Solve the expression for y;
4 - Replace y by f^-1(x).
Let's apply them to the given expression.
[tex]\begin{gathered} y=\frac{1}{3}x+2 \\ x=\frac{1}{3}y+2 \\ \frac{1}{3}y=x-2 \\ y=3x-3\cdot2 \\ y=3x-6 \\ f^{-1}(x)=3x-6 \end{gathered}[/tex]The inverse of the function is "3x - 6".
