f(x)=−13x2−17x+5

Question

g(x)=9x2+8x−16

What is (f+g)(x)
?

(1 point)
Responses

−4x2+9x−21
negative 4 x squared plus 9 x minus 21

−22x2−25x+21
negative 22 x squared minus 25 x plus 21

−4x2−9x−11
negative 4 x squared minus 9 x minus 11

−13x2−11

Answer 1

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

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

Now, we add them together:

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

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

Now, 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:

\[ (f+g)(x) = -4x^2 - 9x - 11 \]

The correct answer is: \(-4x^2 - 9x - 11\) (negative 4 x squared minus 9 x minus 11).