#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.