Suppose the functions f (x) and g (x) are inverse functions. About what line is the graph of g (x) a reflection

of the graph of f (x)

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!

If f (x) and g (x) are inverse functions, their graphs are reflections of one another in the line y=x.