Question

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

\\f(x) = \frac{5x + 2}{x^2 - 81}, \quad g(x) = \frac{4x - 7}{x^2 - 81}\\

(type your answer in interval notation.)

the domain of \\(f-g\\) is \\(\varnothing\\)

\\((fg)(x) = \frac{20x^2 - 27x - 14}{(x^2 - 81)^2}\\) (simplify your answer)

what is the domain of \\(fg\\)?

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

Explanation:

Find the domains of the individual functions

Using the Domain of Rational Functions knowledge point

$$
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Determine the domain of the product function fg

Using the Function Operations and Interval Notation knowledge points

$$
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Answer:

• (A) The domain of fg is \((-\infty, -9) \cup (-9, 9) \cup (9, \infty)\) (Correct answer)
• (B) The domain of fg is { } (Use a comma to separate answers as needed.)
• (C) The domain of fg is \(\varnothing\)