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) = $ (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\

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

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Domain of Polynomials" ], "new_concepts": [ "Function Operations" ], "current_concepts": [ "Domain of Polynomials", "Function Operations" ] } ## Define the functions and operation Using the *Domain of Polynomials* knowledge point $$ \begin{aligned} &f(x) = 6x + 1 \ &g(x) = x - 3 \end{aligned} $$ ## Compute the sum of the functions Using the *Domain of Polynomials* knowledge point $$ \begin{aligned} (f+g)(x) &= f(x) + g(x) \ &= (6x + 1) + (x - 3) \ &= 6x + x + 1 - 3 \ &= 7x - 2 \end{aligned} $$ $(f + g)(x) =$ $7x - 2$ (Simplify your answer.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Function Operations" ] }

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Explanation:

Define the functions and operation

Compute the sum of the functions

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