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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 – 4, g(x) = x2 and h(x) = 3x – 5
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Solution
f(x) = x – 4, g(x) = x2 and h(x) = 3x – 5
(fog)oh = fo(goh)
L.H.S. = (fog)oh
fog = f(g(x)) = f(x2) = x2 – 4
(fog)oh = (fog)(3x – 5) = (3x – 5)2 – 4
= 9x2 – 30x + 25 – 4
= 9x2 – 30x + 21 …(1)
∴ R.H.S. = fo(goh)
(goh) = g(h(x)) = g(3x – 5) = (3x – 5)2
= 9x2 – 30x + 25
fo(goh) = f(9x2 – 30 x + 25)
= 9x2 – 30x + 25 – 4
= 9x2 – 30x + 21 …(2)
(1) = (2)
L.H.S. = R.H.S.
∴ (fog)oh = fo(goh)
It is proved.
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