Question
Download Solution PDFIf f(x) = 4x + 1 and g(x) = kx + 2 such that fog(x) = gof(x), then what is the value of k ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Given: f(x) = 4x + 1 and g(x) = kx + 2 such that fog(x) = gof(x)
fog(x) = f(g(x)) = 4g(x) + 1
⇒ fog(x) = 4(kx + 2) + 1 = 4kx + 9 __-(i)
And gof(x) = g(f(x)) = kf(x) + 2
⇒ gof(x) = k(4x + 1) + 2 = 4kx + k + 2 __(ii)
Since fog(x) = gof(x), so equating (i) and (ii),
⇒ 4kx + 9 = 4kx + k + 2
⇒ 9 = k + 2
⇒ k = 7
∴ The correct option is (1).
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