What is the domain of a function?

[brycenrg]

Homework Statement

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]

 

[Mark44]

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.

 

[brycenrg]

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

 

[Dick]

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?

 

[brycenrg]

Yes thank you, L>5 and L<10 that helped a lot.