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Even or odd function

  1. Oct 29, 2012 #1
    1. The problem statement, all variables and given/known data
    Show that function is even or odd:

    (x^2|x-1|)/(SQRT(x-1)^2)

    2. Relevant equations



    3. The attempt at a solution
    (-x^2|-x-1|)/(SQRT(-x-1)^2)

    After this i dont know how to procede.
     
  2. jcsd
  3. Oct 29, 2012 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    You need to start by using brackets correctly, so you do not end up writing things that are false. First, I assume you mean sqrt[(x-1)^2], and not [sqrt(x-1)]^2 (which is more-or-less what is meant by what you wrote).

    So, if f(x) = x^2 |x-1|/sqrt[(x-1)^2] we have f(-x) = (-x)^2 |-x-1|/sqrt[(-x-1)^2]. Notice that this is not equal to -x^2 |-x-1|/sqrt[(-x-1)^2], which is what you wrote.

    Anyway, now you need to figure out whether or not you have f(x) = f(-x) or f(x) = -f(-x) for all x, or neither.

    When you don't know what to do, try plotting the function; just looking at its graph will tell you a lot.

    RGV
     
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