To find \((F + G)(x)\), we simply need to add the two functions \(F(x)\) and \(G(x)\) together.
Given:
- \(F(x) = -13x^2 - 17x + 5\)
- \(G(x) = 9x^2 + 8x - 16\)
We add them as follows:
\[ (F + G)(x) = F(x) + G(x) \]
Substituting in the expressions for \(F(x)\) and \(G(x)\):
\[ (F + G)(x) = (-13x^2 - 17x + 5) + (9x^2 + 8x - 16) \]
Now, combine like terms:
-
Combine the \(x^2\) terms: \[ -13x^2 + 9x^2 = -4x^2 \]
-
Combine the \(x\) terms: \[ -17x + 8x = -9x \]
-
Combine the constant terms: \[ 5 - 16 = -11 \]
Now, putting it all together:
\[ (F + G)(x) = -4x^2 - 9x - 11 \]
So the final result is:
\[ (F + G)(x) = -4x^2 - 9x - 11 \]
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