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**SlipEternal** Sorry, I was hoping you would see that $\displaystyle f$ brings $\displaystyle x$ to $\displaystyle f(x)$ and both $\displaystyle g,h$ bring it back... so when restricted to the image of $\displaystyle f$, both $\displaystyle g,h$ act as inverse functions. So, try to determine properties for the image of $\displaystyle f$. For instance, assume $\displaystyle sup\{f(x): x \in \mathbb{R}\}=0$ What would $\displaystyle \lim_{t \to 0}{g(t)}$ be? What about $\displaystyle g(1)$? You don't need $\displaystyle f$ to be onto. In fact, it can be extremely discontinuous, and by looking at the properties of its image, then the properties of its inverse, you should be able to quickly arrive at your conclusion.