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Math Help - Discontinuous functions

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by jkru View Post
    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
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by jkru View Post
    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
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  4. #4
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    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.
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  5. #5
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    Found it

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