When y= a constant, how do you find the interval of definition?

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Discussion Overview

The discussion revolves around determining the interval of definition for a differential equation solution that results in a constant value, specifically when y = 3/4. Participants explore the implications of having a constant solution and how it relates to the concept of domain in functions.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant notes that if the solution is y = c, then dy/dt must be 0, suggesting that the solution is valid for all t unless specified otherwise.
  • Another participant proposes that the interval of definition could be (-∞, ∞), questioning how a function can have a domain when it is just a constant.
  • A further reply reiterates that for the function y(t) = 3/4, the domain is determined by the range of t values that can be input, regardless of the constant output.
  • One participant expresses confusion about the terminology, indicating a preference not to use the word "range" when discussing domain to avoid confusion.

Areas of Agreement / Disagreement

Participants generally agree that the interval of definition could be (-∞, ∞), but there is some confusion and debate regarding the terminology and the nature of domains for constant functions.

Contextual Notes

There is a lack of clarity regarding the definitions of domain and range as they pertain to constant functions, and some assumptions about the conditions under which dy/dt = 0 are not fully explored.

Jeff12341234
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I used the linear equation method to solve a D.E. and got y=3/4 at the end. I'm asked to find the interval of definition but I don't know how to do that when Y is just a constant :/
 
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If your solution is y=c then dy/dt must have been 0.
Unless it was specified that dy/dt=0 on some particular interval, then your solution should be valid for all t.
 
So the interval of definition would be (-∞,∞)?

I just don't get how a function can have a domain when it's just a constant...
 
Jeff12341234 said:
So the interval of definition would be (-∞,∞)?

I just don't get how a function can have a domain when it's just a constant...

If your function is y(t) = 3/4, it means that for any t you give the function as an input, the function returns the value 3/4. So, the domain is whatever range of values of t you are allowed to put into your function. It doesn't matter that your function happens to return a constant in this case.
 
thanks
 
Jeff12341234 said:
So the interval of definition would be (-∞,∞)?

I just don't get how a function can have a domain when it's just a constant...
Every function has a domain.
Mute said:
If your function is y(t) = 3/4, it means that for any t you give the function as an input, the function returns the value 3/4. So, the domain is whatever range[/color] of values of t you are allowed to put into your function. It doesn't matter that your function happens to return a constant in this case.
I wouldn't use the word "range" when you're talking about the domain, because of confusing the issue with the function's range.
 

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