To get the inverse of any function f(x) [ just make sure that it passes the horizontal line test] follow the steps:
- Solve for x, i.e separate x in one side and the other terms in the other side, included f(x).
- Swap x and f(x).
- The result is the inverse of the original function [tex]f^{-1}(x)[/tex]
Let's apply that on your case:
[tex][tex]\(\begin{matrix} \\f(x) = 7x-13\\~\\ \\f(x)+13=7x\\~\\ \\ \frac{f(x)+13}{7} =x\\~\\ \\Now~swap\\~\\ \huge\underline{{f^{-1}(x)=\frac{x+13}{7}}} \end{matrix}\) [/tex][/tex]
I hope that helps!
