Given the following:

Question

f(x)=−13x2−17x+5

g(x)=9x2+8x−16

What is (f+g)(x)?

(1 point)
Responses

−4x2+9x−21

−22x2−25x+21

−4x2−9x−11

−13x2−11

Answer 1

To find \((f + g)(x)\), we need to add the functions \(f(x)\) and \(g(x)\) together.

Given: \[ f(x) = -13x^2 - 17x + 5 \] \[ g(x) = 9x^2 + 8x - 16 \]

Now, we can combine them: \[ (f + g)(x) = f(x) + g(x) \] \[ = (-13x^2 - 17x + 5) + (9x^2 + 8x - 16) \]

Now, let's combine like terms:

1. Combine the \(x^2\) terms: \[ -13x^2 + 9x^2 = -4x^2 \]

2. Combine the \(x\) terms: \[ -17x + 8x = -9x \]

3. Combine the constant terms: \[ 5 - 16 = -11 \]

Putting it all together, we have: \[ (f + g)(x) = -4x^2 - 9x - 11 \]

Thus, the final result is: \[ \boxed{-4x^2 - 9x - 11} \]