Question

If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.

Options

• - 9

• 18

• `1/9`

• 9

Answer 1

If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = 9.

Explanation:

We have,

f(x) = 3x + 6, g(x) = 4x + k

Since, fog (x) = gof (x)

⇒ f(g)(x) = g(f(x))

⇒ f(4x + k) = g(3x + 6)

⇒ 3(4x + k) + 6 = 4 (3x + 6) + K

⇒ 3k - k = 24 - 6

⇒ 2k = 18

⇒ k = 9