If f : R → R, g : R → R be two given functions then f (x) = 2 min { f (x) – g (x), 0} equals

We have, f (x) = 2 min { f (x) – g (x), 0}=0                      f(x)>g(x)2[f(x)−g(x)],    f(x)≤g(x) =f(x)−g(x)−|f(x)−g(x)|,    f(x)>g(x)f(x)−g(x)−|f(x)−g(x)|,    f(x)≤g(x)∴ f (x) = f (x) – g (x) –|g (x) – f (x)|