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Question
Find the value of k, such that fog = gof
f(x) = 3x + 2, g(x) = 6x – k
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Solution
f(x) = 3x + 2, g(x) = 6x – k
fog(x) = f(g(x))
= f(6x – k)
= 3(6x – k) + 2
= 18x – 3k + 2 …(1)
gof(x) = g(f(x))
= g(3x + 2)
= 6(3x + 2) – k
= 18x + 12 – k ...(2)
(1) = (2)
⇒ 18x – 3k + 2 = 18x + 12 – k
2k = –10
k = –5
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