Question

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

Explanation:

Step1: Recall the definition of function addition

The sum of two functions \( (f + g)(x) \) is defined as \( f(x) + g(x) \).

Step2: Substitute the given functions

We know \( f(x) = 3x^2 \) and \( g(x) = -3x + 3 \), so we substitute these into the formula for \( (f + g)(x) \):
\( (f + g)(x) = f(x) + g(x) = 3x^2 + (-3x + 3) \)

Step3: Simplify the expression

Remove the parentheses and combine like terms (there are no like terms to combine here, just simplify the sign):
\( (f + g)(x) = 3x^2 - 3x + 3 \)

Answer:

\( 3x^2 - 3x + 3 \)