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

the domain of \\(f+g\\) is \\((-\infty, -9) \cup (-9, 9) \cup (9, \infty)\\).
(type your answer in interval notation.)

c. the domain of \\(f+g\\) is \\(\varnothing\\).

\\((f-g)(x) = \frac{1}{x-9}\\) (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 \\(\quad\\)
(type your answer in interval notation.)

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

Explanation:

Find the domain of the individual functions

Using the Domain of Rational Functions knowledge point

$$
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$$

Determine the domain of the difference function

Using the Function Operations and Interval Notation knowledge points

$$
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$$

Answer:

• A. The domain of \(f - g\) is { } (Use a comma to separate answers as needed.)
• B. The domain of \(f - g\) is \((-\infty, -9) \cup (-9, 9) \cup (9, \infty)\) (Type your answer in interval notation.) (Correct answer)
• C. The domain of \(f - g\) is \(\varnothing\)