#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
9768: #58
Re: 9768: #58
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.