Given f(x)=1|x|−x and g(x)=1x−|x| then
domf≠ϕ and dom g=ϕ
domf=ϕand dom g≠ϕ
f and g have the same domain
dom f=ϕ and dom g=ϕ
domf={x:|x|>x} and dom g={x:x>|x|}= ϕ. Thus dom f=R− (the set of all negative real numbers)and dom g = ϕ.