Answer
$f(f^{-1}(x)) = f^{-1}(f(x)) = x$
In each case, the graph would look like the straight line $y = x$
Work Step by Step
$f(x) = 3x-2$
$f^{-1}(x) = \frac{1}{3}x+\frac{2}{3}$
We can find $f(f^{-1}(x))$:
$f(x) = 3x-2$
$f(f^{-1}(x)) = 3~(\frac{1}{3}x+\frac{2}{3})-2$
$f(f^{-1}(x)) = x+2-2$
$f(f^{-1}(x)) = x$
We can find $f^{-1}(f(x))$:
$f^{-1}(x) = \frac{1}{3}x+\frac{2}{3}$
$f^{-1}(f(x)) = \frac{1}{3}(3x-2)+\frac{2}{3}$
$f^{-1}(f(x)) = x-\frac{2}{3}+\frac{2}{3}$
$f^{-1}(f(x)) = x$
Therefore, $f(f^{-1}(x)) = f^{-1}(f(x)) = x$
In each case, the graph would look like the straight line $y = x$
