Answer
$ r^{-1}(x)=\frac{2x+5}{13}$
Work Step by Step
We are given the function, $r(x)=\frac{13x-5}{2}$. First, we must replace $r(x)$ with y.
$y=\frac{13x-5}{2}$
Next, interchange x and y.
$x=\frac{13y-5}{2}$
Next, multiply both sides by 2.
$2x=13y-5$
Add 5 to both sides.
$13y=2x+5$
Divide both sides by 13.
$y=\frac{2x+5}{13}$
Finally, replace y with $r^{-1}(x)$.
$ r^{-1}(x)=\frac{2x+5}{13}$
