Suppose that g:[0,1] -> [0,1] is a continuous and strictly increasing function such that g(0)=0 and g(1)=1. Under these hypotheses g(x) has an inverse function g^-1 : [0,1] -> [0,1] such that

g^-1(g(x)) =x and g(g^-1(x)) =x for all x E [0,1]

Show that if xf is a fixed point of g(x) then xf is also a fixed point of g^-1(x)
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