One-One Function Homework Help

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Homework Help Overview

The discussion revolves around understanding the concept of one-one functions and determining the largest possible domain for such functions. Participants are exploring the implications of the definition of one-one functions and how it relates to intervals on the horizontal axis.

Discussion Character

  • Conceptual clarification, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are questioning the meaning of "the largest possible" domain and whether it refers to the widest interval or the highest limit. There is also discussion about specific intervals that could be considered one-to-one.

Discussion Status

The conversation includes various interpretations of the intervals that could be valid for one-one functions. Some participants suggest that certain intervals may not be appropriate, while others argue for the validity of their choices. There is an ongoing exploration of the criteria for selecting intervals.

Contextual Notes

Participants are navigating the constraints of the problem, particularly the requirement for the function to be one-to-one over the chosen interval. There is a focus on the characteristics of the function within specified intervals.

LiHJ
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Homework Statement



Dear Mentors and PF helpers,

Please help me to understand this question. Thank you for your time.
[/B]
image.jpg


Homework Equations


My understanding of a one-one function is that if a horizontal line where to intersect the curve, there should be only 1 intersection.[/B]

The Attempt at a Solution


1) My questions is what does "the largest possible" domain means?

Does it mean to find the widest interval between the lower limit and the higher limit? Or does it mean that the upper limit should be as great as possible?
 
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LiHJ said:

Homework Statement



Dear Mentors and PF helpers,

Please help me to understand this question. Thank you for your time.
[/B]
View attachment 77164

Homework Equations


My understanding of a one-one function is that if a horizontal line where to intersect the curve, there should be only 1 intersection.[/B]

The Attempt at a Solution


1) My questions is what does "the largest possible" domain means?

Does it mean to find the widest interval between the lower limit and the higher limit? Or does it mean that the upper limit should be as great as possible?
No, it means the largest interval on the horizontal axis for which the function is one-to-one.
 
Dear Sirs,

Than can the answer be [ pi/4, 3pi/2].

Thank you
 
LiHJ said:
Dear Sirs,

Than can the answer be [ pi/4, 3pi/2].
No, that's too large an interval.
 
Dear Sirs,

Why it is too large an interval? That section that I mentioned is also within the definition of a one one function. Why it is that we have to specifically choose [-pi/4,pi/4], there are many sections to choose as well.
 
LiHJ said:
Dear Sirs,

Why it is too large an interval?
Because your function is not one-to-one on that interval (i.e., on ##[\pi/4, 3\pi/2]##. Did you mean ##[\pi/4, 3\pi/4]## instead?
LiHJ said:
That section that I mentioned is also within the definition of a one one function. Why it is that we have to specifically choose [-pi/4,pi/4], there are many sections to choose as well.
Yes, any interval of the right length will do. What you want is an interval on which the function is either increasing on the entire interval or decreasing on the entire interval.
 
Dear Sirs,

Sorry I typed wrongly, you i mean [ pi/4, 3pi/4 ]. So my answer should be acceptable as well?
 
LiHJ said:
Dear Sirs,

Sorry I typed wrongly, you i mean [ pi/4, 3pi/4 ]. So my answer should be acceptable as well?
I'm not sure. The question was "what is the largest possible domain?" so I think they are looking for an interval length rather than an interval. The length of the largest possible domain is ##\pi/2##.
 
Thank you very much;)
 

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