# proving three different functions

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• September 30th 2012, 12:42 PM
zannagorfe
proving 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
• September 30th 2012, 12:54 PM
Siron
Re: proving three different functions
You need to prove $f=h$ thus $\forall x: f(x)=h(x)$.
So start with $f(x)$ and try to get $h(x)$ using the given information.
• September 30th 2012, 01:14 PM
zannagorfe
Re: proving three different functions
what information? i dont see very much information in this question
• September 30th 2012, 01:39 PM
Plato
Re: proving three different functions
Quote:

Originally Posted by zannagorfe
what information? i dont see very much information in this question

$\forall t$ we have $f[t]=f[g(h(t))]=f(g[h(t)])=h(t)$.

Follow the groupings carefully .