# Math Help - Open and closed sets and functions

1. ## Open and closed sets and functions

Let f->R be continuous. For each of the following, prove or give a counter example:

a) If D is open, then f(D) is open
b) if D is closed, then f(D) is closed
c) If D is unbounded, then f(D) is unbounded
d) If D is finite, then f(D) is finite
e) If D is infinite, then f(d) is infinite.

I need to know counter examples for a,b,c, and e and how to prove d is true.

2. Originally Posted by algebrapro18
a) If D is open, then f(D) is open
False. Consider constant functions.
b) if D is closed, then f(D) is closed
Consider $f(x) = e^{-x}$ and $D = \mathbb{R}$.
c) If D is unbounded, then f(D) is unbounded
Consider constant function.
d) If D is finite, then f(D) is finite
The image of a finite set is always finite.
e) If D is infinite, then f(d) is infinite.
Consider constant functions.