Question

what is (f + g)(x)?
f(x) = 4x + 3
g(x) = x² - 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 \((f + g)(x)=f(x)+g(x)\).

Step2: Substitute the given functions

Substitute \(f(x) = 4x + 3\) and \(g(x)=x^{2}-7x\) into the formula:
\((f + g)(x)=(4x + 3)+(x^{2}-7x)\)

Step3: Combine like terms

First, remove the parentheses: \(4x + 3+x^{2}-7x\).
Then, combine the \(x\)-terms: \(4x-7x=-3x\).
So the expression becomes \(x^{2}-3x + 3\).

Answer:

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