Question

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

\\f(x) = \frac{5x}{x-4}, g(x) = \frac{4}{x+5}\\

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

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

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

what is the domain of \\(f-g\\)?
a. the domain of \\(f-g\\) is (type your answer in interval notation.)

Explanation:

Find the domains of the individual functions

Using the Domain of Rational Functions knowledge point

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Find the sum function and its domain

Using the Function Operations and Interval Notation knowledge points

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Find the difference function and its domain

Using the Function Operations and Interval Notation knowledge points

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Answer:

Question 1

\((f+g)(x) = \frac{5x^2+29x-16}{(x-4)(x+5)}\)

Question 2

The domain of \(f+g\) is A. The domain of \(f+g\) is \((-\infty, -5) \cup (-5, 4) \cup (4, \infty)\).

Question 3

\((f-g)(x) = \frac{5x^2+21x+16}{(x-4)(x+5)}\)

Question 4

The domain of \(f-g\) is A. The domain of \(f-g\) is \((-\infty, -5) \cup (-5, 4) \cup (4, \infty)\).