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Math Help - solution set of f(x)g(x)=0 and (f(x))^2+(g(x))^2=0 given...

  1. #1
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    solution set of f(x)g(x)=0 and (f(x))^2+(g(x))^2=0 given...

    Hi, I have this problem which I don't know how to solve...I don't want the answer, but the properties I need to work it out so that I can apply to other problems (but if I need to be shown with an example, then I don't mind being shown how to solve it). Thanks a lot!

    Let the solution set of f(x)=0 be A and the solution set of g(x)=0 be B. What is the solution set of f(x)g(x)=0? What is the solution set of (f(x))^2+(g(x))^2=0? What relationship holds between the solution set P of f(x)<2 and the solution set Q of f(x)<-1?
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  2. #2
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    f(x)g(x)=0 iff f(x)=0 or g(x)=0 iff x\in A\cup B.


    f(x)<-1\Rightarrow f(x)<2. So Q\subset P.
    Last edited by DrSteve; November 24th 2010 at 09:35 AM.
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  3. #3
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    \left[ {f(x)} \right]^2  + \left[ {g(x)} \right]^2  = 0 if and only if f(x) = 0\;\& \;g(x) = 0 together.
    Therefore that solution set is A\cap B.
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