If two functions are inverse of each other, they are basically switching the x- and y-axes.
Take for example, p(x)=2x, is a line passing through the origin with a slope of two. Its inverse, q(x)=x/2, is a line passing through the origin with a slope of 1/2, the reciprocal of 2. If you plot the two lines, you will notice that the two lines are symmetrical about y=x, or a 45 degree line from the x-axis.
This also explains y=x (which lines on the line of reflection) has its inverse also equal to y=x!
