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Answer:
[tex]f(x)=4x\\g(x)=x+2[/tex]
Step-by-step explanation:
Because we have to rewrite this equation in the format [tex]f(g(x))[/tex], we have to divide, or factor to find basic terms,
Expanding the value of k(x), we have [tex]k(x)=4x+8[/tex]. We see that each term can be divisible by 4, so we can factor out 4 to get
[tex]k(x)=4(x+2)[/tex]
Now, we have two different terms getting multiplied. We can separate the two to get [tex]4 \text{ and} (x+2)[/tex]
Because we are multiplying 4 by the other term, this is represented by [tex]4x[/tex]
Now, we can just set f(x) and g(x) to these functions:
[tex]f(x)=4x\\g(x)=x+2[/tex]
Now, just to make sure, we can plug a value into k(x) and the same value into f(g(x)). Plugging in 1, we have (2(1)+4)2 as 2(2+4), which is 2(6) = 12.
Plugging 1 into f(g(x)), we can evaluate g(1) first, to get 1 + 2 = 3. Now, f(3) = 4(3)= 12, which is the same for k(x).