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The total revenue from the sale of a popular book is approximated by the rational R(x) = 1000x^2/x^2 + 4, where x is the number of years since publication and the total revenue in millions of dollars. Use this function to complete parts a through d. (a) Find the total revenue at the end of the first year. $ million (b) Find the total revenue at the end of the second year. $ million (c) Find the domain of function R. Choose the correct domain below. {x | x is a real number and x greaterthanorequalto 0} {x | x is a real number and x lessthanorequalto 5} {x | x is a real number and x notequalto 2, x notequalto 5} {x | x is a real number and x notequalto 2}

Answer :

Answer:

a) 200 million dollars

b) 500 million dollars

c) Option A)

[tex]\{x|x \in R, x \geq 0\}[/tex]      

Step-by-step explanation:

We are given the following in the question:

[tex]R(x) = \dfrac{1000x^2}{x^2 + 4}[/tex]

where R(x) is the revenue function in millions of dollars and x is the number of years since publication.

a) total revenue at the end of the first year

We put x = 1 in the revenue function

[tex]R(1) = \dfrac{1000(1)^2}{(1)^2 + 4} = 200[/tex]

Thus, the revenue after 1 year is 200 million dollars.

b)  total revenue at the end of the second year

We put x = 2 in the revenue function

[tex]R(2) = \dfrac{1000(2)^2}{(2)^2 + 4} = 500[/tex]

Thus, the revenue after 2 year is 500 million dollars.

c)  domain of function R

Domain:

It is the values of x for which the function R(x) is defined.

Since,

[tex]x^2 + 4 \neq 0, x \in R[/tex]

Thus, it is a proper function.

The domain is given by

Option A)

[tex]\{x|x \in R, x \geq 0\}[/tex]

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