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

1. S is a connected subset of R

2. S is an open subset of R

3. S is a bounded subset of R

I don't know how 1 and 2 are right.

59. A cyclic group 5 has an element x such that the set {x^3, x^5, x^9} has exactly two elements. The number of elements in the set {x^(13n) : n is a positive integer} is

I am not sure my way of thinking is correct. Correct me if I am wrong.

We know that {x^3, x^5, x^9} has exactly two elements, which means {x^3,x^5} are the only two elements and we know the order of x^3 is 3.

Therefore, {x^(13n):n is a positive integer} consists of three elements. They are x^13,x^26, and x^39, correct?