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Question
Find the value of k, such that fog = gof
f(x) = 2x – k, g(x) = 4x + 5
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Solution
f(x) = 2x – k, g(x) = 4x + 5
fog(x) = f(g(x)) = f(4x + 5) = 2(4x + 5) – k
= 8x + 10 – k …(1)
gof(x) = g(f(x)) = g(2x – k) = 4(2x – k) + 5
= 8x – 4k + 5 ...(2)
(1) = (2)
⇒ 8x + 10 – k = 8x – 4k + 5
3k = – 5
k = `(-5)/(3)`
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