Q79 / 150 · MHT CET 2019 (Shift 2) · Mathematics

If $f (x) = 3 x + 6, g (x) = 4 x + k$ and $f o g (x) = g o f (x)$ then k =

A
-9
B
18
C
$\frac{1}{9}$
Correct answer
D
9

Solution

We have,

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

Since,

f o g (x) = g o f (x)

\Rightarrow f (g) x = g (f (x))

\Rightarrow f (4 x + k) = g (3 x + 6)

\Rightarrow 3 (4 x + k) + 6 = 4 (3 x + 6) + K

\Rightarrow 3 k - k = 24 - 6

\Rightarrow 2 k = 18

\Rightarrow k = 9

Hence, the correct answer is option: 'D'.

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