Results 1 to 6 of 6

Math Help - Solution Set Question.

  1. #1
    Newbie
    Joined
    Oct 2010
    Posts
    9

    Question Solution Set Question.

    Hi,

    I'm new to the forum but hope to contribute when and where I can.

    I'm doing some study at the moment and I was stuck on the following problem.

    Help appreciated.

    Let the solution set of f(x)=0 be A and the solution set of g(x)=0 be B (here f and g are real functions taking real values).

    What is the solution sets of f(x)g(x)=0 and of f(x)2+g(x)2=0.


    I'm not sure how this answer is supposed to look.



    My initial thoughts were something along the lines of



    f(x).g(x) = A.B = 0 [A product B]



    and



    f(x)^2 + g(x)^2 = A^2 + B^2 = 0


    But I really don't know if this is going in the right direction at all?


    If you have a minute I would be grateful for your thoughts.


    -Infinite.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,530
    Thanks
    774
    f(x).g(x) = A.B = 0 [A product B]
    This does not make type sense, or at least more explanation is needed. What do you mean by the product of two sets: the Cartesian product or maybe \{xy\mid x\in A, y\in B\}? What does 0 mean: is it a number? Then how can a product of two sets equal a number? Similarly, for what x do you consider f(x)g(x), or is it some product of functions as a whole?

    Try to find a relationship between the propositions f(x) = 0 and f(x)g(x) = 0. Which implies which? What does it say about the relationship between A and the solution set of f(x)g(x) = 0?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,614
    Thanks
    1581
    Awards
    1
    It odd that just this week I have seen the old notation for union and intersection come up on this board. R.L. Moore and many of his students used AB\text{ or }A\cdot B for A\cap B and A+B for A\cup B.
    Quote Originally Posted by infinitepersepctives View Post
    Let the solution set of f(x)=0 be A and the solution set of g(x)=0 be B (here f and g are real functions taking real values).
    What is the solution sets of f(x)g(x)=0 and of f(x)2+g(x)2=0.
    For the solution set of f(x)g(x) it would be A\cup B.

    For the solution set of f^2(x)+g^2(x) it would be A\cap B.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Oct 2010
    Posts
    9
    Thanks for that. Is there a possibility of a short explanation on this?

    For the solution set of f(x)g(x) it would be A\cup B.

    For the solution set of f^2(x)+g^2(x) it would be A\cap B.
    Are these well-known rules rather than a problem exercise?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,614
    Thanks
    1581
    Awards
    1
    It is common sense.
    A\cdot B=0 if and only if A=0\text{ or }B=0. OR is union.

    A^2+ B^2=0 if and only if A=0\text{ and }B=0. AND is intersection.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Oct 2010
    Posts
    9
    Thank you! That makes sense alright! :-) Great!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: November 7th 2011, 03:27 PM
  2. independant solution question
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: November 13th 2010, 10:35 AM
  3. solving for the solution question
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: May 16th 2010, 10:59 AM
  4. Replies: 1
    Last Post: August 29th 2008, 10:17 AM
  5. Solution of the question
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 1st 2007, 04:42 AM

Search Tags


/mathhelpforum @mathhelpforum