Question

if f(x)=3x-2,g(x)=2x+k and if fog =God then find the value of k
​

Answer 1

Answer :

k = -1

Solution :

• Given : f(x) = 3x - 2 , g(x) = 2x + k
• To find : If fog = gof , then k = ?

Now ,

=> fog(x) = f[g(x)]

=> fog(x) = f(2x + k)

=> fog(x) = 3(2x + k) - 2

=> fog(x) = 6x + 3k - 2

Now ,

=> gof(x) = g[f(x)]

=> gof(x) = g(3x - 2)

=> gof(x) = 2(3x - 2) + k

=> gof(x) = 6x - 4 + k

Now ,

According to the question , fog = gof

=> fog(x) = gof(x)

=> 6x + 3k - 2 = 6x - 4 + k

=> 3k - k = 2 - 4

=> 2k = -2

=> k = -2/2

=> k = -1

Hence k = -1 .