Question

what is $(f + g)(x)$?
$f(x) = 4x$
$g(x) = -x^2 + 7x$
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 \(f(x) + g(x)\).
So we substitute the given functions \(f(x)=4x\) and \(g(x)=-x^{2}+7x\) into this formula: \((f + g)(x)=f(x)+g(x)=4x+(-x^{2}+7x)\)

Step2: Combine like terms

First, remove the parentheses: \(4x - x^{2}+7x\)
Then, combine the \(x\)-terms: \(4x + 7x=11x\)
So the expression becomes \(-x^{2}+11x\)

Answer:

\(-x^{2}+11x\)