I didn't know that "g(x) is one to one if and only if g(a)=g(b), etc,". I know that if (a,b)is a point on the graph of y=g(x) then b=g(a), which is equivalent to the statement that [tex] a=g^{1}(b)[/tex], which means that (b,a) is a point on the graph of g_inverse. And that then g and g_inverse are symmetrical about the line y=x.
