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}\\

\\((f+g)(x) = \frac{9x-5}{x^2-81}\\) (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 domains of the individual functions

Using the Domain of Rational Functions knowledge point

$$
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$$

Determine the domain of the sum function

Using the Function Operations knowledge point

$$
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$$

Express the domain in interval notation

Using the Interval Notation knowledge point

$$ (-\infty, -9) \cup (-9, 9) \cup (9, \infty) $$

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 \(\varnothing\)