Question

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

Answer 1

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

Answer 2

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!