Answered

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[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 :

GinnyAnswer
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]
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