1. ## Continuity

Suppose that f and g are functions from a set S to R and that f is continuous at a given number a at which the function g fails to be continuous.
(1) What can be said about the continuity of the function f+g at the number a?
(2) What can be said about the continuity of the function fg at the number a?
(3) What can be said about the continuity of the function fg at the number a if f(a)=0 and g is a bounded function?
(4) What can we say about the continuity of the function fg at the number a if f(a) does not equal 0?

Thanks!

2. Originally Posted by Slazenger3
Suppose that f and g are functions from a set S to R and that f is continuous at a given number a at which the function g fails to be continuous.
(1) What can be said about the continuity of the function f+g at the number a?
(2) What can be said about the continuity of the function fg at the number a?
(3) What can be said about the continuity of the function fg at the number a if f(a)=0 and g is a bounded function?
(4) What can we say about the continuity of the function fg at the number a if f(a) does not equal 0?

Thanks!
What do you think?

For 2) how about $\displaystyle f(x)=x$ and $\displaystyle g(x)=\begin{cases}\frac{1}{x} & \mbox{if}\quad x\ne 0 \\ 1 & \mbox{if}\quad x=0\end{cases}$