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]
