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Determining if a function is odd or even

  • Thread starter ainster31
  • Start date
  • #1
157
1

Homework Statement



t1dk1L2.png


Homework Equations





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.
 

Answers and Replies

  • #2
pasmith
Homework Helper
1,740
412

Homework Statement



t1dk1L2.png


Homework Equations





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.
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.)
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,833
955

Homework Statement



t1dk1L2.png


Homework Equations





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.
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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