9768: #58
Posted: 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
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