Question

f(x) = 3x + 2, g(x) = 6x - k find fog = gof and 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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Step-by-step explanation:

Answer 2

The value of k is -5.

Step-by-step explanation:

Given : $f(x) = 3x + 2$ and $g(x) = 6x - k$,  fog = gof

To find : The value of k​ ?

Solution :

We know,

$fog(x)=f(g(x))$

$fog(x)=f(6x - k)$

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

$fog(x)=18x - 3k+2$

Similarly,

$gof(x)=g(f(x))$

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

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

$gof(x)=18x+12-k$

Now,

$fog(x)=gof(x)$

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

$-3k+k=12-2$

$-2k=10$

$k=\frac{-10}{2}$

$k=-5$

Therefore, the value of k is -5.

#Learn more

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

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