Question

let $f(x) = 3x + 4$ and $g(x) = 2x - 7$. find $(f + g)(x)$, $(f - g)(x)$, $(fg)(x)$, and $left(\frac{f}{g}\
ight)(x)$. give the domain of each.

$(f + g)(x) = \square$ (simplify your answer.)

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

Given \(f(x) = 3x + 4\) and \(g(x)=2x - 7\), substitute these into the formula:
\((f + g)(x)=(3x + 4)+(2x - 7)\)

Step3: Combine like terms

Combine the \(x\)-terms and the constant terms:
\(3x+2x=5x\) and \(4 - 7=-3\), so \((f + g)(x)=5x-3\).

Answer:

\(5x - 3\)