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
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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) $\displaystyle f(x)=\begin{cases} -1, & x=0 \\ x, & x\not= 0 \end{cases}$ $\displaystyle g(x)=\begin{cases} +1, & x=0 \\ 0, & x\not= 0 \end{cases}$ $\displaystyle f(x)+g(x)=\begin{cases} -1+1 = 0, & x=0 \\ x, & x\not= 0 \end{cases} = x$ f and g are not continious in x=0
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 $\displaystyle f=-g$ And consider $\displaystyle f=g^{-1}$ If that does not suffice I can give you more specific examples
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.
Never mind. I just found an f and g that worked. Thanks!
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