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Determining if a function is odd or even

  1. Oct 23, 2013 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations

    3. The attempt at a solution

    $$f(-x)=\begin{cases} -x+5,\quad -2<x<0 \\ x+5,\quad 0≤x<2 \end{cases}\\ =f(x)$$

    The issue is that I can't get to the second step. I know the function is even.
  2. jcsd
  3. Oct 23, 2013 #2


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    Homework Helper

    You should have
    $$f(-x)=\begin{cases} -x+5,\quad -2<-x<0 \\ x+5,\quad 0≤-x<2 \end{cases}$$

    (You need to substitute -x for x in the inequalities as well.)
  4. Oct 24, 2013 #3


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    Science Advisor

    I have no idea what you mean by "the second step". (What was the first step?) Just use the definition of "even function".

    If -2< x< 0 then 0< x< 2 so f(-x)= (-x)+ 5= -x+ 5= f(x).
    If 0< x< 2 then -2< x< 0 so f(-x)= -(-x)+ 5= x+ 5= f(x).
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