Question

Prove the formulas
\(\Large{\max(a,b)=\frac{a+b+|a-b|}{2}}\), \(\Large{\min(a,b)=\frac{a+b-|a-b|}{2}}\)
for \( a,b \in\mathbb{R}\). Show as a corollary: For continuous functions
\(f,g:X\rightarrow \mathbb{R}\) on a metric space \(X\) the function
\(\max(f,g):X\rightarrow \mathbb{R}\) defined by \(\max(f,g)(x)=\max(f(g),g(x)\),
is continuous as well. Analogously for \(\min(f,g)\).