Question

what is (f + g)(x)?
f(x) = 2x + 2
g(x) = x
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 that \(f(x) = 2x + 2\) and \(g(x)=x\). So we substitute these into the formula for the sum:
\((f + g)(x)=f(x)+g(x)=(2x + 2)+x\)

Step3: Combine like terms

Combine the \(x\)-terms: \(2x+x = 3x\), and the constant term remains \(2\). So \((f + g)(x)=3x + 2\)

Answer:

\(3x + 2\)