Question

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

Answer 1

Answer:Given

fog=gof

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

f(6x-k)=g(3x+2)

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

18x-3k+2=18x+12-k

-2k=10

k=-5

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Answer 2

The value of k is 1.

Given,

Two functions f(x) = 3x+2 and g(x) = 2x+k.

Also, fog = gof

To Find,

The value of k.

Solution,

First, we will find the function fog and gof

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

Now,

f(x) = 3x+2

f(2x+k) = 3(2x+k)+2 = 6x+3k+2

gof = g(f(x)) = g(3x+2)

g(x) = 2x+k

g(3x+2) = 2(3x+2)+k = 6x+4+k

Now,

fog = gof

So,

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

2k = 2

k = 1

Hence, the value of k is 1.

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