Is this a valid representation of a function in Lambda Calculus?
It's valid (because it respects $\lambda$-calculus syntax) but won't work as you expect. To see that just take your favorite language and try it out:

let f = \x -&gt; 2*x
let g = \y -&gt; y+1
let h = \z -&gt; z/2


(\x -&gt; (((fx)g)h))) 1 won't evaluate to $1.5$. Why? 

Because $g$ and $h$ are functions and take one argument each, and application happens when there's an abstraction to the left. So if you change the order you will get the expected behavior. 

$$ \lambda x. (h (g (f ~ x))) $$

or 

$$ \lambda x. ((h  \circ g  \circ f)  ~ x) $$

In Haskell:

(\x -&gt; (h . g . f) x)


where . ($\circ$) is for function composition.

Example:

$$ \big(\lambda x. (h (g (f ~ x)))\big) 1  \rightarrow (h (g (f ~ 1))) \rightarrow (h (g ~ 2)) \rightarrow  (h ~ 3) \rightarrow 1.5 $$