Question

For the given functions f(n) = n² + 4n and g(n) = -n - 5, find f(n) + g(n).

Answer 1

To sum the functions f(n) = n² + 4n and g(n) = -n - 5, like terms are combined to result in f(n) + g(n) = n² + 3n - 5.

Step-by-step explanation:

To find the sum of the two functions f(n) and g(n), we must evaluate f(n) + g(n). Given the functions f(n) = n² + 4n and g(n) = -n - 5, we can combine like n terms and constants.

Let's proceed step by step:

1. First write down the given functions f(n) and g(n).
2. Then, sum the functions by adding the corresponding terms. Add the n² term of f(n) with the n term of g(n), and add the constant term of f(n) with the constant term of g(n).

The sum is:

f(n) + g(n) = (n² + 4n) + (-n - 5)

Simplify by adding like terms:

f(n) + g(n) = n² + 4n - n - 5 = n² + 3n - 5

The combined function after adding f(n) to g(n) is n² + 3n - 5.