Question

Given that k(x) = (2x + 4)2

Answer 1

Answer:

$f(x)=4x\\g(x)=x+2$

Step-by-step explanation:

Because we have to rewrite this equation in the format $f(g(x))$, we have to divide, or factor to find basic terms,

Expanding the value of k(x), we have $k(x)=4x+8$. We see that each term can be divisible by 4, so we can factor out 4 to get

$k(x)=4(x+2)$

Now, we have two different terms getting multiplied. We can separate the two to get $4 \text{ and} (x+2)$

Because we are multiplying 4 by the other term, this is represented by $4x$

Now, we can just set f(x) and g(x) to these functions:

$f(x)=4x\\g(x)=x+2$

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).