Question

The function q = 230,000 -28p is a demand function which expresses the quantity demanded of a product q as a function of the price charged for the product p, stated in dollars. Determine the restricted Domain and Range of the function.
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Answer 1

Answer:

Domain,   0<p<8214.28

Range,     0<f(p)<230000

Given:

The function q = f(p) = 230000 - 28p

To find:

Restricted Domain and Range of the function.

Solution:

f(p) = 230000 - 28p

For domain, f(p) = 230000 - 28p >0

                          = 230000>28p

                           = 230,000/28 >p

                           = 8214.28>p

                           = f(p) < 8214.28

so, Domain,  0<p<8214.28

      Range,   0<f(p)<230000

Answer 2

Final Answer:

The restricted Domain and Range of the demand function$q=230000-28p$, which expresses the quantity demanded of a product q as a function of the price charged for the product p, stated in dollars are $0 < p < 8214.29$ and $0 < q < 230000$ respectively.

Given:

The demand function is

$q=230000-28p$.

This demand function expresses the quantity demanded of a product q in terms of a function of the price charged for the product p, stated in dollars.

To Find:

The restricted Domain and Range of the demand function

$q=230000-28p$ is to be calculated.

Explanation:

A function can have one or more variables which may be dependent or independent. Whenever there is an independent variable present in an equation, it is possible to express the equation as a function of that independent variable.

Note the following important points.

The variation of the values of the independent variable from its minimum possible value to its maximum allowable value defines the restricted domain of the function and the corresponding variation of the function itself describes the range of the function.

Step 1 of 3

Here, in the demand function $q=230000-28p$,  p is the price charged for the product, stated in dollars and q is the quantity demanded of the product.

So, p is the independent variable and q is a function of the independent variable p.

Thus, the values of p determines the restricted Domain of the demand function, while the corresponding values of q dictates the Range of the demand function $q=230000-28p$.

Step 2 of 3

By the problem q must be greater than zero.

So, it follows these calculations gradually.

$q > 0\\230000-28p > 0\\-28p > -230000\\28p < 230000\\p < \frac{230000}{28}\\p < 8214.29$

Step 3 of 3

Since the price of the product must be greater than zero, the following is true.

$p > 0\\0 < p$

Hence, the restricted domain of the demand function$q=230000-28p$, is as follows

$0 < p < 8214.29$

Note that the variation of p as given by  $8214.29 > p > 0$, governs the following variation of q.

$0 < q < 230000$

So the Range of the demand function$q=230000-28p$ is given by the inequality $0 < q < 230000$.

Therefore, the restricted Domain and Range of the demand function

$q=230000-28p$ are $0 < p < 8214.29$ and $0 < q < 230000$ respectively, where p is the price charged for the product, stated in dollars and q is the quantity demanded of the product.

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