Question

Given the following:

f(x)=−13x2−17x+5
𝑓
(
𝑥
)
=
−
13
𝑥
2
−
17
𝑥
+
5

g(x)=9x2+8x−16
𝑔
(
𝑥
)
=
9
𝑥
2
+
8
𝑥
−
16

What is (f+g)(x)
(
𝑓
+
𝑔
)
(
𝑥
)
?

(1 point)
Responses

−4x2+9x−21
−
4
𝑥
2
+
9
𝑥
−
21
negative 4 x squared plus 9 x minus 21

−22x2−25x+21
−
22
𝑥
2
−
25
𝑥
+
21
negative 22 x squared minus 25 x plus 21

−4x2−9x−11
−
4
𝑥
2
−
9
𝑥
−
11
negative 4 x squared minus 9 x minus 11

−13x2−11

Answer 1

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

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

Now, let's add \(f(x)\) and \(g(x)\):

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

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

Now, combine like terms:

1. **Quadratic terms**: \(-13x^2 + 9x^2 = -4x^2\)
2. **Linear terms**: \(-17x + 8x = -9x\)
3. **Constant terms**: \(5 - 16 = -11\)

Putting these together:

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

So, the answer is:

\(-4x^2 - 9x - 11\) (which matches the response option: \(−4x^2−9x−11\)).