Q. 10

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 for all x, y, z ∈ N. Show that ho (gof) = (hog) of.

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

((hog)of)(x) = (hog)(f(x))= (hog)(2x)

=h(g(2x))=h(3(2x) + 4)

=h(6x + 4) = sin(6x + 4) x N

This shows, ho(gof) = (hog)of

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