Continuity problems for my Analysis class

LauraLovies
I am having a lot of difficulty on my continuity problems for my Analysis class.

1. Prove that (f O g)(x) = f(g(x)) is continuous at any point p in R in three ways a.) Using the episolon delta definition of continuity, b.) using the sequence definition of continuity, and c.) using the open set definition of continuity.

2. Prove that if U is an open set in R, then its inverse is open.

Homework Helper
Hi LauraLovies!

(I assume f and g are both continuous? and have a delta: δ and an epsilon: ε )

Show us what you've tried, and where you're stuck, and then we'll know how to help!

LauraLovies

f and g are both continuous so i know that there exists some $$\epsilon > 0 and greater than zero that fulfills the continuity definition. It just seems to obvious to me that i dont even know where to start. \delta$$