Question

given f(x) = x + 1 and g(x) = 3x - 1, evaluate ea

1. (f + g)(x)

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 \(f(x)=x + 1\) and \(g(x)=3x - 1\), so substitute these into the formula:
\((f + g)(x)=f(x)+g(x)=(x + 1)+(3x - 1)\)

Step3: Combine like terms

First, remove the parentheses: \(x + 1+3x - 1\). Then combine the \(x\)-terms and the constant terms:
\(x+3x=4x\) and \(1 - 1 = 0\). So \((f + g)(x)=4x\)

Answer:

\(4x\)