Question

If f : X → Y, g : Y → Z and h : Z → S are functions, thenho(gof) = (hog) o f.​

Answer 1

Proof :We have

ho(gof) (x) = h(gof(x)) = h(g(f(x))), ∀ x in X

and (hog) of (x) = hog(f (x)) = h(g(f(x))), ∀ x in X.Hence, ho(gof) = (hog) o f.