# Math Help - proving three different functions

1. ## 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.

2. ## 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.

3. ## Re: proving three different functions

what information? i dont see very much information in this question

4. ## Re: proving three different functions

Originally Posted by zannagorfe
what information? i dont see very much information in this question
$\forall t$ we have $f[t]=f[g(h(t))]=f(g[h(t)])=h(t)$.