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.)

$(fg)(x) = 6x^2 - 13x - 28$ (simplify your answer.)

$left(\frac{f}{g}\
ight)(x) = \frac{3x + 4}{2x - 7}$ (simplify your answer.)

the domain of $f + g$ is \\(\square\\).
(type your answer in interval notation.)

Explanation:

Step1: Analyze (f+g)(x)

The function \((f + g)(x)=5x - 3\) is a linear function. Linear functions are polynomials of degree 1, and the domain of a linear function (polynomial) is all real numbers because there are no restrictions (no division by zero, no square roots of negative numbers, etc.) for any real value of \(x\).

Step2: Write domain in interval notation

The set of all real numbers in interval notation is \((-\infty,\infty)\).

Answer:

\((-\infty,\infty)\)