Answered

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Subtract:

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

a. [tex]\(2x^2 + 2x - 11\)[/tex]

b. [tex]\(-2x^2 - 2x - 11\)[/tex]

c. [tex]\(2x^2 - 2x + 11\)[/tex]

d. [tex]\(-2x^2 + 2x + 11\)[/tex]

Sagot :

GinnyAnswer
To solve the problem of subtracting the function [tex]\( g(x) \)[/tex] from [tex]\( f(x) \)[/tex], we need to follow these steps:

1. Write down the functions:
[tex]\[ f(x) = -5x^2 + x - 2 \][/tex]
[tex]\[ g(x) = -3x^2 + 3x + 9 \][/tex]

2. Subtract [tex]\( g(x) \)[/tex] from [tex]\( f(x) \)[/tex]:
[tex]\[ f(x) - g(x) = (-5x^2 + x - 2) - (-3x^2 + 3x + 9) \][/tex]

3. Distribute the negative sign across [tex]\( g(x) \)[/tex]:
[tex]\[ f(x) - g(x) = -5x^2 + x - 2 - (-3x^2 + 3x + 9) \][/tex]
[tex]\[ f(x) - g(x) = -5x^2 + x - 2 + 3x^2 - 3x - 9 \][/tex]

4. Combine like terms:
- Combine the [tex]\( x^2 \)[/tex] terms:
[tex]\[ -5x^2 + 3x^2 = -2x^2 \][/tex]

- Combine the [tex]\( x \)[/tex] terms:
[tex]\[ x - 3x = -2x \][/tex]

- Combine the constant terms:
[tex]\[ -2 - 9 = -11 \][/tex]

5. Write down the final result:
[tex]\[ f(x) - g(x) = -2x^2 - 2x - 11 \][/tex]

The correct choice is:
[tex]\[ \boxed{-2 x^2-2 x-11} \][/tex]
Thus, the correct answer is (b) [tex]\( -2 x^2 - 2 x - 11 \)[/tex].
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