Homework Help: (Real Analysis) Find sets E\F and f(E)\f(F)

1. Aug 28, 2010

phillyolly

1. The problem statement, all variables and given/known data

The problem #11.

3. 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.

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2. Aug 29, 2010

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

3. Aug 29, 2010

vela

Staff Emeritus
f(E) = {f(x) | x ∈ E}

Does that make sense?

4. Aug 29, 2010

phillyolly

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

5. Aug 29, 2010

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.

6. Aug 29, 2010

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.

7. Aug 29, 2010

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

8. Aug 29, 2010

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.

9. Aug 29, 2010

vela

Staff Emeritus
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.