f(x) = 5x + 2; g(x) = 2x – 3; h(x) = 3x + 1
L.H.S. = fo(goh)
goh = g[h(x)]
= g(3x + 1)
= 2(3x + 1) – 3
= 6x – 1
fo(goh) = f[goh(x)]
= f(6x – 1)
= 5(6x – 1) + 2
= 30 x – 5 + 2
fo(goh) = 30x – 3 … (1)
R.H.S. = (fog)oh
fog = f[g(x)]
= f(2x – 3)
= 5(2x – 3) + 2
= 30x – 5 + 2
fo(goh) = 30x – 3 …..(1)
R.H.S. = (fog) oh
fog = f[g(x)]
= f(2x – 3)
= 5 (2x – 3)
= 5 (2x – 3) + 2
= 10x – 15 + 2
= 10x – 13
(fog) oh = fog [h(x)]
= fog (3x + 1)
= 10 (3x + 1) – 13
= 30x + 10 – 13
= 30x – 3 … (2)
From (1) and (2) we get L.H.S. = R.H.S.
fo(goh) = (fog)oh
