Implement $\max$ with a closed form expression?

Question

I have 2 functions: $f(x)$ and $g(x)$. Both of them range in $[0,1]$.

Is there some way to define a $h(x)$ that efficiently takes the greater one of $h(x)$ and $g(x)$, i.e. $h(x) = \max \{ f(x),g(x) \}$, but without using $\max$?

If there is no exact solution, an approximate $h(x)$ is also fine.

Answer 1

Since you ask for alternatives, note that $$\max\{s,t\}=\tfrac12s+\tfrac12t+\tfrac12|s-t|, $$ and that, if one also wants to avoid absolute values, $$\max\{s,t\}=\tfrac12s+\tfrac12t+\tfrac12\sqrt{t^2+s^2-2st}. $$ Both these formulas are actually less handy than the maximum you started from (the square-root formula being probably even less handy than the absolute-value one)...