Find the image of a piecewise continuous function

[TheReMiXeR]

We were given a terrible example and we as a whole group cannot solve this task, please help us solve it

 

[blamocur]

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What have you tried?

Which definition of the function's image do you have?

 

[pka]

We were given a terrible example and we as a whole group cannot solve this task, please help us solve it

I agree that the given attachment is terrible. We are given no real directions.
The title of the thread is totally misleading. The function is not continuous.
Nowhere at we given what [imath]a~\&~b[/imath] are, let alone what what purpose they both serve?
What do the the symbols [imath]\pi\rho\mathcal{H}[/imath] in the attachment mean?

 

[Dr.Peterson]

I agree that the given attachment is terrible. We are given no real directions.
The title of the thread is totally misleading. The function is not continuous.
Nowhere at we given what [imath]a~\&~b[/imath] are, let alone what what purpose they both serve?
What do the the symbols [imath]\pi\rho\mathcal{H}[/imath] in the attachment mean?

Actually, the function is piecewise continuous, which is what it says; and what you read as [imath]\pi\rho\mathcal{H}[/imath] is Russian, and presumably means something like "for" or "when". (Google says "at".)

My question is in the opposite direction: Why would they have any trouble with this question?

We were given a terrible example and we as a whole group cannot solve this task, please help us solve it

Can you show us the "terrible example" you say you were given prior to this problem, and what ideas different people have?

To me the problem is fairly simple, but I can easily imagine some questions you might have struggled with, particularly if you had not seen anything quite like this. The more you can tell us of your thinking, the better we can help.

 

[TheReMiXeR]

Actually, the function is piecewise continuous, which is what it says; and what you read as [imath]\pi\rho\mathcal{H}[/imath] is Russian, and presumably means something like "for" or "when". (Google says "at".)

My question is in the opposite direction: Why would they have any trouble with this question?


Can you show us the "terrible example" you say you were given prior to this problem, and what ideas different people have?

To me the problem is fairly simple, but I can easily imagine some questions you might have struggled with, particularly if you had not seen anything quite like this. The more you can tell us of your thinking, the better we can help.

Here
Sorry for not replying for a long time, I have a lot of tasks piled on me (

 

[Dr.Peterson]

Here
Sorry for not replying for a long time, I have a lot of tasks piled on me (

The translation (and OCR, which for example changes t₀ to 1) is not very good, but what's more important is that you have not told us the context; what does "f -> F" refer to, for example?

I don't see that this has anything to do with the problem you asked about (about the image of a function) -- unless perhaps it is asking about the image of the function in an entirely different sense than I have assumed, and wants the "image" of f under whatever transformation the example is about. In that case, what is most important is the context of the question. What subject are you studying?

If you had responded by telling us what ideas you and your group have had, we would be much further along.

Please ask specific questions about the problem, so we can answer them.

 

[TheReMiXeR]

The translation (and OCR, which for example changes t₀ to 1) is not very good, but what's more important is that you have not told us the context; what does "f -> F" refer to, for example?

I don't see that this has anything to do with the problem you asked about (about the image of a function) -- unless perhaps it is asking about the image of the function in an entirely different sense than I have assumed, and wants the "image" of f under whatever transformation the example is about. In that case, what is most important is the context of the question. What subject are you studying?

If you had responded by telling us what ideas you and your group have had, we would be much further along.

Please ask specific questions about the problem, so we can answer them.

That's literally all we were given... After the black line is an explanation of the theorem that should be used to solve this problem (in the solution they refer to 1-2.5, this is it), I just combined the solution with the theorem into one file.
I myself do not understand how this is calculated, I said that the example is bad (