![\boxed{A. \ f(g(2)) = -7 \ }](https://tex.z-dn.net/?f=%5Cboxed%7BA.%20%5C%20f%28g%282%29%29%20%3D%20-7%20%5C%20%7D)
<h3>Further explanation</h3>
In this problem we will find out the value of the function composition. There are two ways to do it.
![\boxed{ \ f(x) = x + 8 \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20f%28x%29%20%3D%20x%20%2B%208%20%5C%20%7D)
![\boxed{ \ g(x) = x^2 - 6x - 7 \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20g%28x%29%20%3D%20x%5E2%20-%206x%20-%207%20%5C%20%7D)
![\boxed{ \ f(g(2)) = ? \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20f%28g%282%29%29%20%3D%20%3F%20%5C%20%7D)
First way
Step-1: compose (f o g)(x) = f(g(x))
Here g(x) as input into f(x). In other words, first we apply g(x), then apply f(x) to that result:
![g(x) = x^2 - 6x - 7 \rightarrow f(x) = x+8](https://tex.z-dn.net/?f=g%28x%29%20%3D%20x%5E2%20-%206x%20-%207%20%5Crightarrow%20f%28x%29%20%3D%20x%2B8)
![f(g(x)) = (x^2 - 6x - 7) + 8](https://tex.z-dn.net/?f=f%28g%28x%29%29%20%3D%20%28x%5E2%20-%206x%20-%207%29%20%2B%208)
![f(g(x)) = x^2 - 6x - 7 + 8](https://tex.z-dn.net/?f=f%28g%28x%29%29%20%3D%20x%5E2%20-%206x%20-%207%20%2B%208)
And we get,
![\boxed{ \ f(g(x)) = x^2 - 6x + 1 \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20f%28g%28x%29%29%20%3D%20x%5E2%20-%206x%20%2B%201%20%5C%20%7D)
Step-2: calculate the value of f(g(2))
After getting f(g(x)) we proceed by calculating the value f (g(2)).
![x = 2 \rightarrow f(g(2)) = (2)^2 - 6(2) + 1](https://tex.z-dn.net/?f=x%20%3D%202%20%5Crightarrow%20f%28g%282%29%29%20%3D%20%282%29%5E2%20-%206%282%29%20%2B%201)
![f(g(2)) = 4 - 12 + 1](https://tex.z-dn.net/?f=%20f%28g%282%29%29%20%3D%204%20-%2012%20%2B%201)
And we obtain the final result:
![\boxed{ \ f(g(2)) = -7 \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20f%28g%282%29%29%20%3D%20-7%20%5C%20%7D)
Second way
Step-1: count g(2) initially
![x = 2 \rightarrow g(2) = (2)^2 - 6(2) - 7](https://tex.z-dn.net/?f=x%20%3D%202%20%5Crightarrow%20g%282%29%20%3D%20%282%29%5E2%20-%206%282%29%20-%207)
![g(2) = 4 - 12 - 7](https://tex.z-dn.net/?f=%20g%282%29%20%3D%204%20-%2012%20-%207%20)
And we get,
![\boxed{ \ g(2) = -15 \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20g%282%29%20%3D%20-15%20%5C%20%7D)
Step-2: calculate the value of f(g(2))
Here the value of g(2), i.e. -15, as input into f(x).
![g(2) = -15 \rightarrow f(-15) = -15 + 8](https://tex.z-dn.net/?f=g%282%29%20%3D%20-15%20%5Crightarrow%20f%28-15%29%20%3D%20-15%20%2B%208)
And we obtain the final result:
![\boxed{ \ f(g(2)) = -7 \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20f%28g%282%29%29%20%3D%20-7%20%5C%20%7D)
<h3>Learn more</h3>
- Let f(x) = x-3 and g(x ) = x^2 find f(g(4)) brainly.com/question/1052893
- Which expression is equal to f(x) · g(x)? brainly.com/question/9622736
- Find (f - g)(x) and its domain brainly.com/question/12000925
Keywords: Let f(x) = x + 8 and g(x) = x² - 6x - 7, find f(g(2)), composition function, input, f(g(x)), value, initially,