Question

If f (x) = 3x − 2 , g(x) = 2x + k and f o g = g o f , then find the value of k.

• A. 1
• B. -1
• C. -2
• D. 2

Answer 1

The correct option is B -1

Given: f (x) = 3x − 2 and g(x) = 2x + k
Now, f o g(x) = f (g(x))
= f (2x +k)
= 3(2x +k)−2
$\Rightarrow$ f o g(x) = 6x + 3k −2
Also, g o f (x) = g (f(x))
= g(3x −2)
= 2(3x −2)+k
$\therefore$ g o f (x) = 6x - 4 + k
But, f o g = g o f
$\Rightarrow$ 6x + 3k −2 = 6x - 4 + k
$\Rightarrow$ 2k = -2
$\Rightarrow$ k = -1
Hence, value of k is -1.