1. ## Discontinuous functions

Give an example of a function f and g such that both are discontinuous at some value c in the Reals and

a.)the sum f+g is continuous at c

b.)the product fg is continuous at c

2. Originally Posted by jkru
Give an example of a function f and g such that both are discontinuous at some value c in the Reals and

a.)the sum f+g is continuous at c

b.)the product fg is continuous at c

a)

$f(x)=\begin{cases} -1, & x=0 \\ x, & x\not= 0 \end{cases}$
$g(x)=\begin{cases} +1, & x=0 \\ 0, & x\not= 0 \end{cases}$

$f(x)+g(x)=\begin{cases} -1+1 = 0, & x=0 \\ x, & x\not= 0 \end{cases} = x$

f and g are not continious in x=0

3. Originally Posted by jkru
Give an example of a function f and g such that both are discontinuous at some value c in the Reals and

a.)the sum f+g is continuous at c

b.)the product fg is continuous at c
$f=-g$

And consider $f=g^{-1}$

If that does not suffice I can give you more specific examples

4. ## f = g^-1

I've tried a couple different equations like you suggested, but I am unable to get equations that are discontinuous at the same value. Any tips on how pick equations so this will happen? Thanks for your help.

5. ## Found it

Never mind. I just found an f and g that worked. Thanks!