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Math Help - Even and Odd Functions.. HELP!

  1. #1
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    Exclamation Even and Odd Functions.. HELP!

    hello!
    i was randomly searching things about functions and i was teaching myself domain and range. i understand those.
    however, i don't understand even and odd functions

    i understand the basic ones like x^2 |x| and cos x are even and x^3 sinx and tanx are odd..
    i was wondering what these were:
    f(x)= 2^x
    f(x)= log base 2 x
    f(x)= square root of x
    and f(x)= square root of a^2 - x^2

    thank you!
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  2. #2
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    If f(-x) = f(x) the function is even.

    If f(-x) = -f(x) the function is odd.

    If neither occurs, it is neither even nor odd.
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  3. #3
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    So now you need to think:

    1) Are 2^x and 2^{-x} the same? (If so the function is even.) Are they the same except that one is positive and the other negative? (If so the function is odd.) If neither of those is true , the function is neither even nor odd.
    (If they are not the same you can show it by this one "counter-example". If an example show they are the same, you will need to look for a general way to show they are always the same. You might try graphing the functions.)

    2) Same questions. Are log_2(x) and log_2(-x) the same? Are they even both defined?!

    3) Are \sqrt{x} and \sqrt{-x} the same? Are they even both defined?

    4) Are \sqrt{a^2- x^2} and \sqrt{a^2- (-x)^2} the same?
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