Question

Let f(x) = 7x − 13. Find f^−1(x)

Answer 1

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
`f^(-1)(x)`

Let's apply that on your case:

`[tex]\(\begin{matrix} \\f(x) = 7x-13\\~\\ \\f(x)+13=7x\\~\\ \\ (f(x)+13)/(7) =x\\~\\ \\Now~swap\\~\\ \huge\underline{{f^(-1)(x)=(x+13)/(7)}} \end{matrix}\)`[/tex]

And that is it :)

I hope that helps!