find $f+g$, $f-g$, $fg$ and $\frac{f}{g}$. determine the domain for each function.

$f(x) = 6x + 1$, $g(x) = x - 3$

b. the domain of $f+g$ is $\{\quad\}$. (use a comma to separate answers as needed.)
c. the domain of $f+g$ is $\varnothing$.

$(f-g)(x) = 5x + 4$ (simplify your answer.)

what is the domain of $f-g$?

a. the domain of $f-g$ is $(-\infty, \infty)$. (type your answer in interval notation.)
b. the domain of $f-g$ is $\{\quad\}$. (use a comma to separate answers as needed.)
c. the domain of $f-g$ is $\varnothing$.

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

Question

find $f+g$, $f-g$, $fg$ and $\frac{f}{g}$. determine the domain for each function.

$f(x) = 6x + 1$, $g(x) = x - 3$

b. the domain of $f+g$ is $\{\quad\}$. (use a comma to separate answers as needed.)
c. the domain of $f+g$ is $\varnothing$.

$(f-g)(x) = 5x + 4$ (simplify your answer.)

what is the domain of $f-g$?

a. the domain of $f-g$ is $(-\infty, \infty)$. (type your answer in interval notation.)
b. the domain of $f-g$ is $\{\quad\}$. (use a comma to separate answers as needed.)
c. the domain of $f-g$ is $\varnothing$.

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

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Domain of Polynomials", "Function Operations" ], "new_concepts": [], "current_concepts": [ "Domain of Polynomials", "Function Operations" ] } ## Find the product function $$ (fg)(x) = f(x) \cdot g(x) = (6x + 1)(x - 3) $$ $$ (fg)(x) = 6x^2 - 18x + x - 3 = 6x^2 - 17x - 3 $$ $(fg)(x) =$ $6x^2 - 17x - 3$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Function Operations" ] }

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Find the product function

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