One-One Function Homework Help

  • Thread starter Thread starter LiHJ
  • Start date Start date
  • Tags Tags
    Function
AI Thread Summary
The discussion centers on understanding the concept of a one-one function and determining the largest possible domain for such a function. A one-one function is defined by the property that any horizontal line intersects the curve at most once. The participants clarify that "the largest possible" domain refers to the longest interval on the horizontal axis where the function remains one-to-one. It is emphasized that the interval must be chosen such that the function is either entirely increasing or decreasing within that range. The correct interval length for the largest possible domain is identified as π/2.
LiHJ
Messages
43
Reaction score
2

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?
 
Physics news on Phys.org
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;)
 
Back
Top