Let f, g, h be functions each with range of R, such that f(g(x)) = x and g(h(x)) = x. Prove that f = h.

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- Sep 30th 2012, 12:42 PMzannagorfeproving three different functions
Let f, g, h be functions each with range of R, such that f(g(x)) = x and g(h(x)) = x. Prove that f = h.

Thanks for your help - Sep 30th 2012, 12:54 PMSironRe: proving three different functions
You need to prove $\displaystyle f=h$ thus $\displaystyle \forall x: f(x)=h(x)$.

So start with $\displaystyle f(x)$ and try to get $\displaystyle h(x)$ using the given information. - Sep 30th 2012, 01:14 PMzannagorfeRe: proving three different functions
what information? i dont see very much information in this question

- Sep 30th 2012, 01:39 PMPlatoRe: proving three different functions