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.)

$(f - g)(x) = x + 11$ (simplify your answer.)

$(fg)(x) = \square$ (simplify your answer.)

Explanation:

Step1: Recall the definition of (fg)(x)

The product of two functions \( (fg)(x) \) is defined as \( f(x) \cdot g(x) \). So we need to multiply \( f(x) = 3x + 4 \) and \( g(x) = 2x - 7 \).

Step2: Multiply the two functions

Using the distributive property (FOIL method for binomials), we have:

$$
LATEXBLOCK0
$$

Answer:

\( 6x^2 - 13x - 28 \)