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\\

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) = 2x^2 - 18x + 40\\) (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 Polynomials knowledge point

$$
LATEXBLOCK0
$$

Determine the domain of the difference function

Using the Function Operations and Interval Notation knowledge points

$$
LATEXBLOCK1
$$

Answer:

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