Question

let $f(x) = 7x + 5$ and $g(x) = 2x - 7$. find $(f + g)(x)$, $(f - g)(x)$, $(fg)(x)$, and $left(\frac{f}{g}\
ight)(x)$. give the

$(f + g)(x) = 9x - 2$ (simplify your answer.)

$(f - g)(x) = 5x + 12$ (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 \( f(x) = 7x + 5 \) and \( g(x) = 2x - 7 \).

Step2: Apply the distributive property (FOIL method)

$$
LATEXBLOCK0
$$

Step3: Combine like terms

Combine the middle terms \( -49x \) and \( 10x \):

$$ 14x^{2}+(-49x + 10x)-35=14x^{2}-39x - 35 $$

Answer:

\( 14x^2 - 39x - 35 \)