Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

[tex]$
\begin{array}{l}
f(x)=5x^2+9x-4 \\
g(x)=-8x^2-3x-4
\end{array}
$[/tex]

Find [tex]$(f+g)(x)$[/tex].

A. [tex]$3x^2+6x-8$[/tex]
B. [tex]$-3x^4+6x^2-8$[/tex]
C. [tex]$-3x^3+6x^2-8x$[/tex]
D. [tex]$-3x^2+6x-8$[/tex]


Sagot :

To find [tex]\((f + g)(x)\)[/tex], we need to sum the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]. We are given:

[tex]\[ f(x) = 5x^2 + 9x - 4 \][/tex]
[tex]\[ g(x) = -8x^2 - 3x - 4 \][/tex]

Now, we sum [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] term by term.

1. Sum the [tex]\(x^2\)[/tex] terms:
[tex]\[ 5x^2 + (-8x^2) = 5x^2 - 8x^2 = -3x^2 \][/tex]

2. Sum the [tex]\(x\)[/tex] terms:
[tex]\[ 9x + (-3x) = 9x - 3x = 6x \][/tex]

3. Sum the constant terms:
[tex]\[ -4 + (-4) = -4 - 4 = -8 \][/tex]

Now, putting these results together, we get:

[tex]\[ (f + g)(x) = -3x^2 + 6x - 8 \][/tex]

Thus, the correct answer is:
[tex]\[ \boxed{-3x^2 + 6x - 8} \][/tex]