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If f(x) = 4x + 1 and g(x) = kx + 2 such that fog(x) = gof(x), then what is the value of k ?

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NDA 02/2022 Mathematics Official Paper (Held On 04 Sep 2022)
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  1. 7
  2. 5
  3. 4
  4. 3

Answer (Detailed Solution Below)

Option 1 : 7
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Detailed Solution

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Explanation:

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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