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Question
If f(x)= x2, g(x) = 3x and h(x) = x – 2 Prove that (fog)oh = fo(goh)
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Solution
f(x) = x2
g(x) = 3x
h(x) = x – 2
(fog)oh = x – 2
L.H.S. = fo(goh)
fog = f(g(x))
= f(3x)
= (3x)2
= 9x2
(fog)oh = (fog)[h(x)]
= (fog) (x – 2)
= 9(x – 2)2
= 9(x2 – 4x + 4)
= 9x2 – 36x + 36 ...(1)
R.H.S. = fo(goh)
(goh) = g[h(x)]
= g(x – 2)
= 3(x – 2)
= 3x – 6
fo(goh) = fo[goh(x)]
= f(3x – 6)
= (3x – 6)2
= 9x2 – 36x + 36 ...(2)
From (1) and (2) we get
L.H.S. = R.H.S.
(fog)oh = fo(goh) is proved.
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