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

\f(x) = 2x^2 - 17x + 36, \quad g(x) = x - 4\

$(f + g)(x) = 2x^2 - 16x + 32$ (simplify your answer.)

what is the domain of $f + g$?

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

$(f - g)(x) = \square$ (simplify your answer.)

Question

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

\f(x) = 2x^2 - 17x + 36, \quad g(x) = x - 4\

$(f + g)(x) = 2x^2 - 16x + 32$ (simplify your answer.)

what is the domain of $f + g$?

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

$(f - g)(x) = \square$ (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": [ "Function Operations" ], "new_concepts": [], "current_concepts": [ "Function Operations", "Domain of Polynomials" ] } ## Calculate the difference function $$ \begin{aligned} (f-g)(x) &= f(x) - g(x) \ &= (2x^2 - 17x + 36) - (x - 4) \ &= 2x^2 - 17x + 36 - x + 4 \ &= 2x^2 - 18x + 40 \end{aligned} $$ $(f - g)(x) =$ $2x^2 - 18x + 40$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Function Operations" ] }

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Calculate the difference function

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