Inverse of the composition of two functions If I have a composition of two functions:
$$y = f(g(x),h(x))$$
where both $g(x)$ and $h(x)$ are readily invertible, can I find the inverse of the composition? i.e.: Can I find $x = f^{-1}(y)$? I know this is generally possible for the the composition of one function. 
Perhaps there is a special form of f that permits this?
Thanks

EDIT: Previous answer used the accepted definition of 'composition'. I am trying to interpret what the OP means by composition... I think he means that $f$ is a formula e.g. something like $f(\sin x,e^x)=\sin x\sqrt{e^x}$ means that $f(x,y)=x\sqrt{y}$.
Let $f:\mathbb{R}^2\rightarrow \mathbb{R}$, $g:\mathbb{R}\rightarrow \mathbb{R}$ and $h:\mathbb{R}\rightarrow \mathbb{R}$ be invertible maps.
Define a function $F:\mathbb{R}\rightarrow \mathbb{R}$ by
$$y=F(x)=f(g(x),h(x)).$$
Then $F$ is invertible with
$$x=F^{-1}(y)=g^{-1}\left(\pi_1\left(f^{-1}(y)\right)\right)=h^{-1}\left(\pi_2\left(f^{-1}(y)\right)\right),$$
where $\pi_i:\mathbb{R}^2\rightarrow\mathbb{R}$ is the projection onto the $i$-th factor of $\mathbb{R}^2$.
