Question

2. If f(x) = (x + 2) and g(x) = x + 5, then
(f9)(x) =
Ax? + 7x + 10
Bx2 - 7x + 10

Answer 1

To find the composition of functions f(x) and g(x), plug g(x) into f(x) and simplify. The resulting function, (f ∘ g)(x), equals x+7, which is not listed in the provided answer choices.

Step-by-step explanation:

The question asks us to compose two functions, f(x) and g(x), where f(x) = (x + 2) and g(x) = x + 5. To do this, we need to find the result of f(g(x)), which is often denoted as (f ∘ g)(x). This operation involves taking the function g(x) and plugging it into f(x).

Let's perform this step by step:

1. First, write out the function f(x) replacing x with g(x): f(g(x)) = (g(x) + 2).
2. Knowing that g(x) = x + 5, replace g(x) in the equation: f(g(x)) = ((x + 5) + 2).
3. Simplify the right-hand side: f(g(x)) = x + 5 + 2 = x + 7.
4. Now that we have the simplified form x + 7, we can see that neither option A (Ax^2 + 7x + 10) nor option B (Bx^2 - 7x + 10) matches the result.
5. Therefore, the correct composition of the functions (f ∘ g)(x) is x + 7, and this option doesn't seem to be listed in the provided choices.