Question

f(x)=−13x2−17x+5

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).