Dev has a monthly food budget of $182. He maps the amount of money,x, he spends each month to the number of food items he buys. What are the constrains on the domain?

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joaobezerra joaobezerra · Answer 1 · 2021-12-22T12:22:00+01:00

Using it's concept, it is found that the domain of the function is [tex]0 \leq x \leq 182[/tex], that is, the constraints are:

The domain of a function is the set that contains all possible values for the functions.

In this problem, the input of the function is how much he spends on food.

His budget is of $182, hence, considering this and the fact that he cannot spend a negative amount on food, the constraints are that x is between $0 and his budget of $182(inclusive), and the domain is [tex]0 \leq x \leq 182[/tex].

To learn more about the domain of functions, you can take a look at https://brainly.com/question/25897115

MrRoyal MrRoyal · Answer 2 · 2021-12-23T11:23:16+01:00

The domain of a function is the set of input values the function can have.

The constraints on the domain are: the amount (x) is at least $0, and it is at most $182

From the question, Dev's budget on food is given as:

[tex]Budget = \$182[/tex]

This means that, he cannot spend more than $182.

Represent the amount with x.

So, we have:

[tex]x \le 182[/tex]

Also, he cannot spend a negative amount.

So, we have:

[tex]x \ge 0[/tex]

So, the domain is:

[tex]x \ge 0[/tex] and [tex]x \le 182[/tex]

Rewrite as:

[tex]0 \le x[/tex] and [tex]x \le 182[/tex]

Combine both inequalities

[tex]0 \le x \le 182[/tex]

Hence, the constraints on the domain are: the amount (x) is at least $0, and it is at most $182