(Real Analysis) Find sets E\F and f(E)\f(F)

[phillyolly]

Homework Statement

The problem #11.

The Attempt at a Solution

My partial answer is attached. There, I found E\F. I still don't understand what is f(E) and f(F) and how to derive them from E and F.

 

[Raskolnikov]

From #10 we know that f(E) = f(F). Thus, f(E)\f(F) = {} = $$\emptyset.$$ Can you get the rest?

 

[vela]

f(E) = {f(x) | x ∈ E}

Does that make sense?

 

[phillyolly]

From #10 we know that f(E) = f(F). Thus, f(E)\f(F) = {} = $$\emptyset.$$ Can you get the rest?

So f(E\F) is (-1=<x<0), which is NOT a subset of an empty set.
Correct??

 

[Raskolnikov]

Not quite...almost there.

E\F = { -1 =< x < 0 }, not f(E\F). Find f(E\F). The final step's still the same and obvious.

 

[phillyolly]

My inability to understand is killing me. I am using this forum non-stop for the last 12 hours for Real Analysis questions. No progress on my part what so ever.

 

[Raskolnikov]

How are you going about teaching this to yourself? Which textbook are you using? Any other resources?

 

[phillyolly]

I only have one textbook, which is Real Analysis by Bartle and Sherbert. I've read the chapter many times and continue reading it. Thanks to your, Raskolnikov, comments, I have made some progress, but still very weak.
I also have another online book. I haven't found any helpful online sources for dummies on Real Analysis.

 

[vela]

E is a subset of the domain of the function f. f(E) is a subset of the codomain of f. It's the set that f maps elements of E onto.

If y is an element of f(E), then there's some x in E such that f(x)=y.