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Question
Consider the function f(x), g(x), h(x) as given below. Show that (fog)oh = fo(goh)
f(x) = x2, g(x) = 2x and h(x) = x + 4
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Solution
f(x) = x2, g(x) = 2x and h(x) = x + 4
(fog)oh = fo(goh)
L.H.S. = (fog)oh
fog = f(g(x)) = f(2x) = (2x)2 = 4x2
(fog)oh = (fog) h(x) = (fog) (x + 4)
= 4(x + 4)2 = 4(x2 + 8x +16)
= 4x2 + 32x + 64 …(1)
R.H.S. = fo(goh) goh = g(h(x)) = g(x + 4)
= 2(x + 4) = (2x + 8)
fo(goh) = f(goh) = f(2x + 8) = (2x + 8)2
= 4x2 + 32x + 64 …(2)
(1) = (2)
L.H.S. = R.H.S.
∴ (fog)oh = fo(goh) It is proved.
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