What is the domain of a function?

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In summary, the conversation is about finding the domain for a problem involving length and width. The key to the answer is an inequality that states the length must be greater than the width. Without this restriction, the domain would be [0,10], but to ensure positive numbers, the domain becomes (0,10). The specific answer of (5,10) is obtained by solving the inequalities L>5 and L<10.
  • #1
brycenrg
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Homework Statement



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Homework Equations



How do you find the domain?

The Attempt at a Solution


I figure (1,10) makes sense because it can't be 0 because its needs a quantity to exist. Right?
I see they came up wit 5, but how did they get 5 exactly? They say its just because its bigger than W like length is bigger than width. Does not explain why it would be exactly [5,10]
 
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  • #2
brycenrg said:

Homework Statement



View attachment 67380

Homework Equations



How do you find the domain?

The Attempt at a Solution


I figure (1,10) makes sense because it can't be 0 because its needs a quantity to exist. Right?
I see they came up wit 5, but how did they get 5 exactly? They say its just because its bigger than W like length is bigger than width. Does not explain why it would be exactly [5,10]
The key to their answer is the sentence: Assume that the length is longer than the width. Without this restriction, the domain would be [0, 10]. This would give an area of 0 for L = 0 or L = 10. If you restrict the area to being positive numbers, the domain is then (0, 10). Your answer of (1, 10) doesn't take into account the possibility of the width being less than 1.

In terms of the variables of this problem, what inequality does length > width represent? That's how they got their answer.
 
  • #3
Good point (0,10) includes less than 1, Thank you.

I understand that, they got instead of 0,10 because L is > than W they say the domain is (5,10) but why is it 5? Why not 4 or 6 or 4.2 I am just wondering how they got 5 exactly
 
  • #4
brycenrg said:
Good point (0,10) includes less than 1, Thank you.

I understand that, they got instead of 0,10 because L is > than W they say the domain is (5,10) but why is it 5? Why not 4 or 6 or 4.2 I am just wondering how they got 5 exactly

Since the width is 10-L and the length is L you want L>10-L and 10-L>0. Can you solve those inequalities?
 
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  • #5
Yes thank you, L>5 and L<10 that helped a lot.
 

FAQ: What is the domain of a function?

What is the domain in a scientific study?

The domain in a scientific study refers to the specific area or subject that is being studied. It is the scope or range of the research, and it helps to define the boundaries of the study.

How do you determine the domain of a research project?

The domain of a research project can be determined by identifying the central research question or hypothesis. This question or hypothesis will guide the focus of the study and help to define the domain.

Why is it important to identify the domain in a scientific study?

Identifying the domain in a scientific study is important because it helps to ensure that the research is focused and relevant. It also allows other scientists to understand the context of the study and its potential applications or limitations.

Can the domain of a research project change during the course of the study?

Yes, the domain of a research project can change during the course of the study. As new information is gathered and analyzed, the focus of the research may shift and the domain may need to be redefined.

How can a broad domain affect the validity of a scientific study?

A broad domain can affect the validity of a scientific study by making it difficult to draw specific conclusions. If the scope of the study is too broad, the results may not be applicable to a specific area or subject, and the findings may lack accuracy and precision.

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