Quote by HallsofIvy
Given function f, let [itex]f_e(x)= (f(x)+ f(x))/2[/itex] and [itex]f_o(x)= (f(x) f(x))/2[/itex].

yes f(x)=((f(x)+f(−x))/2 )+(f(x)−f(−x))/2) then (f(x)+f(−x))/2 is even and (f(x)−f(−x))/2 is odd,then i don't know how to argue their continuity and differentiability?