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

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

$(f+g)(x) = 7x - 2$ (simplify your answer.)

what is the domain of $f+g$?

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

Question

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

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

$(f+g)(x) = 7x - 2$ (simplify your answer.)

what is the domain of $f+g$?

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

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Domain of Polynomials", "Interval Notation", "Function Operations" ], "new_concepts": [], "current_concepts": [ "Domain of Polynomials", "Interval Notation", "Function Operations" ] } ## Find the domain of the individual functions Using the *Domain of Polynomials* and *Function Operations* knowledge points $$ \begin{aligned} &f(x) = 6x + 1 \implies D_f = (-\infty, \infty)\ &g(x) = x - 3 \implies D_g = (-\infty, \infty) \end{aligned} $$ ## Determine the domain of the sum function Using the *Function Operations* and *Interval Notation* knowledge points $$ \begin{aligned} &D_{f+g} = D_f \cap D_g\ &D_{f+g} = (-\infty, \infty) \cap (-\infty, \infty) = (-\infty, \infty) \end{aligned} $$

(A) The domain of $f + g$ is $(-\infty, \infty)$

(B) The domain of $f + g$ is $\{\}$

(C) The domain of $f + g$ is $\varnothing$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Domain of Polynomials" ] }

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Explanation:

Find the domain of the individual functions

Determine the domain of the sum function

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