Let f, g and h be functions from R to R. Show that (f + g) oh = foh + goh (f . g) oh = (foh) . (goh)

solution:

LHS = (f + g) gracious

= (f+g)(h(x))

= f(h(x)) + g(h(x))

= foh + goh

= RHS

Once more,

LHS = (f . g) gracious

= f.g(h(x))

= f(h(x)) . g(h(x))

= (foh) . (goh)

= RHS