To find \((f+g)(x)\), we need to add the functions \(f(x)\) and \(g(x)\).
Given: \[ f(x) = -13x^2 - 17x + 5 \] \[ g(x) = 9x^2 + 8x - 16 \]
Now, we add them together:
\[ (f+g)(x) = f(x) + g(x) \]
\[ (f+g)(x) = (-13x^2 - 17x + 5) + (9x^2 + 8x - 16) \]
Now, combine like terms:
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Combine the \(x^2\) terms: \[ -13x^2 + 9x^2 = -4x^2 \]
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Combine the \(x\) terms: \[ -17x + 8x = -9x \]
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Combine the constant terms: \[ 5 - 16 = -11 \]
Putting it all together:
\[ (f+g)(x) = -4x^2 - 9x - 11 \]
The correct answer is: \(-4x^2 - 9x - 11\) (negative 4 x squared minus 9 x minus 11).