Question

Let f(x)=2x−1 and g(x)=x2+2. Determine (f∘g)(−4). Please simplify your answer.

A. (f∘g)(−4)=−23
B. (f∘g)(−4)=14
C. (f∘g)(−4)=−21
D. (f∘g)(−4)=−15

Answer 1

To find (f∘g)(–4), we first calculate g(-4) as 18, then apply f to 18 to get 35.

Step-by-step explanation:

The question asks us to find the value of the composite function (f∘g)(–4). This means we first evaluate g at -4 and then apply the function f to that result. Function g(x) is defined as x^2 + 2, so first we calculate g(-4) which gives us (-4)^2 + 2, equaling 16 + 2, resulting in 18. Next, we take that result and plug it into f(x), which is 2x – 1. Thus, we get f(g(-4)) which is f(18), leading to 2(18) – 1 = 36 – 1, which simplifies to 35. Therefore, the answer is (f∘g)(–4) = 35.