Question

PLEASE ANSWER THIS ITS VERY IMPORTANT

The function f(x) = x + 5 represents the number of animals adopted at one shelter, where x is the number of months.



The function g(x) = 4x + 7 represents the number of animals adopted at another shelter, where x is the number of months.



Part A: What is (f + g)(x)? Show all necessary steps. (2 points)



Part B: Evaluate (f + g)(4). Show your work. (2 points)



Part C: Explain what your answer represents in terms of the scenario. (2 points)

Answer 1

1. Combined Function: \( (f + g)(x) = 5x + 12 \).

2. Evaluation: \( (f + g)(4) = 32 \) represents the total number of animals adopted at both shelters after 4 months.

3. Interpretation: The result signifies the overall impact of both shelters on animal adoptions at the specified time.

Part A: Finding \( (f + g)(x) \)

\[ (f + g)(x) = f(x) + g(x) \]

Substitute the given functions:

\[ (f + g)(x) = (x + 5) + (4x + 7) \]

Combine like terms:

\[ (f + g)(x) = 5x + 12 \]

So, \( (f + g)(x) = 5x + 12 \).

Part B: Evaluating \( (f + g)(4) \)

Substitute \( x = 4 \) into \( (f + g)(x) \):

\[ (f + g)(4) = 5(4) + 12 \]

\[ (f + g)(4) = 20 + 12 \]

\[ (f + g)(4) = 32 \]

Part C: Explanation

\( (f + g)(4) = 32 \) represents the combined number of animals adopted at both shelters after 4 months. Adding the values of \( f(x) \) and \( g(x) \) at this specific time point gives the total number of adoptions. In this scenario, 32 animals were adopted after 4 months when considering both shelters.