Question

what is (f + g)(x)?
f(x) = -3x²
g(x) = 2x² + 7x
write your answer as a polynomial or a rational function in simplest form.

Explanation:

Step1: Recall the definition of function addition

To find \((f + g)(x)\), we use the definition \((f + g)(x)=f(x)+g(x)\).
Given \(f(x)=-3x^{2}\) and \(g(x) = 2x^{2}+7x\), we substitute these into the formula:
\((f + g)(x)=(-3x^{2})+(2x^{2}+7x)\)

Step2: Combine like terms

Combine the \(x^{2}\) terms: \(-3x^{2}+2x^{2}=(-3 + 2)x^{2}=-x^{2}\)
The \(7x\) term remains as it is since there are no other \(x\) - terms to combine with it.
So, \((f + g)(x)=-x^{2}+7x\)

Answer:

\(-x^{2}+7x\)