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Math Help - Functions

  1. #1
    Member roshanhero's Avatar
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    Functions

    Let f_1(x) and f_2(x) be odd and even functions respectively. How can we construct an even function out of these?
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  2. #2
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    Plenty of ways, but why can't you just take f_2(x) as the even function? What's the point of using f_1(x) in constructing an even function?

    Edit: In case you mean you need to construct an even function from only f_1(x), some simple ways would be to take the absolute value or square the function.

    g(x)=|f_1(x)|

    h(x)=(f_1(x))^2

    These would both be even functions.
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  3. #3
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    What does "construct out of them" mean?
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  4. #4
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    Quote Originally Posted by drumist View Post
    Plenty of ways, but why can't you just take f_2(x) as the even function? What's the point of using f_1(x) in constructing an even function?

    Edit: In case you mean you need to construct an even function from only f_1(x), some simple ways would be to take the absolute value or square the function.

    g(x)=|f_1(x)|

    h(x)=(f_1(x))^2

    These would both be even functions.
    And if you really have to use both functions, so would |f_1(x)|+ f_2(x) and (f_1(x))^2+ f_2(x).

    Now, if the problem had been to construct an even function from two odd functions, that would have been a little more interesting!
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  5. #5
    Member Mathelogician's Avatar
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    Also their composition{ g(x) = f1(f2(x)) and h(x) = f2(f1(x)) } are even!
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