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.

$(f + g)(x) = 5x - 3$ (simplify your answer.)

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

Explanation:

Step1: Recall the definition of (f - g)(x)

The difference of two functions \( (f - g)(x) \) is defined as \( f(x) - g(x) \).
Given \( f(x) = 3x + 4 \) and \( g(x) = 2x - 7 \), we substitute these into the formula:
\( (f - g)(x)=f(x)-g(x)=(3x + 4)-(2x - 7) \)

Step2: Simplify the expression

Distribute the negative sign to the terms in \( g(x) \):
\( (3x + 4)-(2x - 7)=3x + 4 - 2x + 7 \)
Combine like terms:
\( (3x - 2x)+(4 + 7)=x + 11 \)

Answer:

\( x + 11 \)