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Question
Using the function f and g given below, find fog and gof. Check whether fog = gof
f(x) = 4x2 – 1, g(x) = 1 + x
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Solution
f(x) = 4x2 – 1, g(x) = 1 + x
fog = f[g(x)]
= 4(1 + x)
= 4(1 + x)2 – 1
= 4[1 + x2 + 2x] – 1
= 4 + 4x2 + 8x – 1
= 4x2 + 8x + 3
gof = g[f(x)]
= g(4x2 – 1)
= 1 + 4x2 – 1
= 4x2
fog ≠ gof
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