Question

Consider f : N → N, g : N → N and h : N → R defined as f(x) = 2x,g (y) = 3y + 4 and h (z) = sin z, ∀ x, y and z in N. Show that ho(gof) = (hog) of.​

Answer 1

$\huge\star\mathfrak\pink{{Answer:-}}$

Solution :

We have

ho(gof) (x) = h(gof (x)) = h(g(f(x))) = h(g (2x))

= h(3(2x) + 4) = h(6x + 4) = sin (6x + 4) ∀ ∈x N.

Also, ((hog) o f ) (x) = (hog) (f(x)) = (hog) (2x) = h ( g (2x))

= h(3(2x) + 4) = h(6x + 4) = sin (6x + 4), ∀ x ∈ N.

This shows that ho(gof) = (hog) o f.This result is true in general situation as well.