Question

what is (s + q)(x)?
s(x) = x²
q(x) = 5x + 5
write your answer as a polynomial or a rational function in simplest form.

Explanation:

Step1: Recall function addition rule

To find \((s + q)(x)\), we use the rule \((s + q)(x)=s(x)+q(x)\).

Step2: Substitute the given functions

We know \(s(x) = x^{2}\) and \(q(x)=5x + 5\). So, substitute these into the addition formula:
\((s + q)(x)=x^{2}+(5x + 5)\)

Step3: Simplify the expression

Remove the parentheses and combine like terms (there are no like terms to combine here, so we just arrange the terms):
\((s + q)(x)=x^{2}+5x + 5\)

Answer:

\(x^{2}+5x + 5\)