Question

Let f, g : R → R be two functions defined as f (x) = |x |+ x and g (x) =| x| – x ∀ x ∈ R. Then, find f o g and g o f.

Answer 1

$(f\circ g)(x)=||x|-x|+|x|-x=|x|-x+|x|-x=2|x|-2x\\(g\circ f)(x)=||x|+x|-(|x|+x)=|x|+x-|x|-x=0$