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Given [tex]f(x) = 11 - 6x[/tex] and [tex]g(x) = -2x^2 + 3x - 4[/tex], find [tex]f(x) + g(x)[/tex].

A. [tex]f(x) + g(x) = -2x^2 - 3x + 7[/tex]
B. [tex]f(x) + g(x) = -2x^2 - 3x - 15[/tex]
C. [tex]f(x) + g(x) = 2x^2 + 9x - 15[/tex]
D. [tex]f(x) + g(x) = 2x^2 - 3x + 7[/tex]

Sagot :

GinnyAnswer
Let's find \( f(x) + g(x) \) given the functions \( f(x) \) and \( g(x) \).

Given:
[tex]\[ f(x) = 11 - 6x \][/tex]
[tex]\[ g(x) = -2x^2 + 3x - 4 \][/tex]

To find \( f(x) + g(x) \), we simply add the two functions together:
[tex]\[ f(x) + g(x) = (11 - 6x) + (-2x^2 + 3x - 4) \][/tex]

Now, let's combine the like terms:

1. Combine the \(x^2\) terms: There is only one \(x^2\) term, which is \(-2x^2\).
2. Combine the \(x\) terms: \(-6x + 3x = -3x\).
3. Combine the constant terms: \(11 - 4 = 7\).

Putting it all together gives us:
[tex]\[ f(x) + g(x) = -2x^2 - 3x + 7 \][/tex]

Therefore, the correct answer is:
[tex]\[ -2x^2 - 3x + 7 \][/tex]

From the given choices, the correct option is:
[tex]\[ f(x) + g(x) = -2x^2 - 3x + 7 \][/tex]
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