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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) = x – 1, g(x) = 3x + 1 and h(x) = x2
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Solution
f(x) = x – 1, g(x) = 3x + 1 and h(x) = x2
f(x) = x – 1
g(x) = 3x + 1
f(x) = x2
(fog)oh = fo(goh)
L.H.S. = (fog)oh
fog = f(g(x)) = f(3x + 1) = 3x + 1 – 1 = 3x
(fog)oh = (fog)(h(x)) = (fog)(x2) = 32 …(1)
R.H.S. = fo(goh)
goh = g(h(x)) = g(x2) = 3x2 + 1
fo(goh) = f(3x2 + 1) = 3x2 + 1 – 1 = 3x2 …(2)
L.H.S. = R.H.S. Hence it is verified.
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