Ok but allow my humble self to use [tex]y[/tex] instead of [tex]f(x)[/tex].
We have,
[tex]y=7x-13[/tex]
If you wanna know what the inverse is swap the values of x and y,
[tex]x=7y-13[/tex]
And now solve for y,
[tex]x+13=7y\implies\boxed{y=f^{-1}(x)=\frac{x+13}{7}}[/tex].
Hope this helps.
