9768: #58

Forum for the GRE subject test in mathematics.
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YKM
Posts: 45
Joined: Mon Aug 08, 2011 10:25 am

9768: #58

Post by YKM » Tue Sep 13, 2011 9:24 am

#58

Let f be a real-valued function defined and continuous on the set of real numbers R. Which of the following must be true of the set S = {f(c): 0 < c < 1} ?

I: S is an connected subset of R
II: S is an open subset of R
III: S is a bounded subset of R

Ans: C: I and III.

My view:
I don't think S is bounded becasue if we let f = 1/x, then S is a unbounded set.


Anyone has any views on this?

Thanks

YKM
Posts: 45
Joined: Mon Aug 08, 2011 10:25 am

Re: 9768: #58

Post by YKM » Tue Sep 13, 2011 9:46 am

I guess I misread the question as it says f is defined and continuous on the whole real line. So the function f = 1/x should not be under consideration as it is undefined at zero.



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