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Math Help - Solving even and odd functions algebraically!

  1. #1
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    Solving even and odd functions algebraically!

    Solving even and odd functions algebraically is what's kicking my butt at the moment. I have to, algebraically of course, determine if an equation is considered even, odd, or neither. But I need help on this question!

     <br />
f(x) = \frac {x}{x^2 - 1}<br />

    NEED! HELP!
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  2. #2
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    Quote Originally Posted by Monkiwrench View Post
    Solving even and odd functions algebraically is what's kicking my butt at the moment. I have to, algebraically of course, determine if an equation is considered even, odd, or neither. But I need help on this question!

     <br />
f(x) = \frac {x}{x^2 - 1}<br />

    NEED! HELP!
    i thought you said you could do this one. replace x with -x and see what happens
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  3. #3
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    Alright Jhevon. Hold my hand and walk me through this one...

    1st step: Aim for an even function using f(-x)!

    Here we go!

     <br />
f(x) = \frac{x}{x^2-1} = \frac{-x}{-x^2-1} = \frac{-x}{x-1} \ne \frac{x}{x^2 - 1}<br />

    Therefore it's not even.

    Right so far, Jhevon?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Monkiwrench View Post
    Alright Jhevon. Hold my hand and walk me through this one...

    1st step: Aim for an even function using f(-x)!

    Here we go!

     <br />
f(x) = \frac{x}{x^2-1} = \frac{-x}{-x^2-1} = \frac{-x}{x-1} \ne \frac{x}{x^2 - 1}<br />

    Therefore it's not even.

    Right so far, Jhevon?
    no, it's not right. what you wrote makes no sense. you right f(x) and then you equate it to something that's not f(x) then you lose the square form the x in the denominator, that is just all types of wrong. i did several of these questions for you. examine them carefully and see what i did, i assure you, i did nothing of the sort that you did here
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  5. #5
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    Okay, well. That's the reason why I wanted you to do a single problem step by step so I can see what I do wrong and whatnot. Because if I'm doing THIS single step wrong, all my answers are wrong, ya know?

    So I'm learning the long way, why don't you just do this problem, and from what I learn, I'll do another problem?

    Seem fair?
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Monkiwrench View Post
    Okay, well. That's the reason why I wanted you to do a single problem step by step so I can see what I do wrong and whatnot. Because if I'm doing THIS single step wrong, all my answers are wrong, ya know?

    So I'm learning the long way, why don't you just do this problem, and from what I learn, I'll do another problem?

    Seem fair?
    no it doesn't seem fair, and here's why. i actually did what you asked, i did several problems for you already, i tested x^2, x^3, \sqrt {x}, \sqrt [3] {x}, \mbox { and } x^2 - x for you, step by step. evidently it didn't help you. that's why i need you to do this on your own. look on all those that i have done before, if you get it wrong i will comment on it, if you get it correct i'll let you know
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  7. #7
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    Alright, gotcha. Just give me a min.
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  8. #8
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    ALRIGHT! For some reason, it's giving me an error and it won't go through. But anyways! Moving on! f(-x) = -f(x), making it an Even Function. Right?

    f(x) = \frac{x}{x^2 - 1}

    f(-x) = \frac{-x}{-x^2 - 1} = \frac{-x}{x^2 - 1}

    -f(x) = \frac{x}{x^2 - 1} = \frac{-x}{x^2 - 1}
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  9. #9
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    Quote Originally Posted by Monkiwrench View Post
    Alright Jhevon. Hold my hand and walk me through this one...

    1st step: Aim for an even function using f(-x)!

    Here we go!

     <br />
f(x) = \frac{x}{x^2-1} = \frac{-x}{-x^2-1} = \frac{-x}{x-1} \ne \frac{x}{x^2 - 1}<br />

    Therefore it's not even.

    Right so far, Jhevon?
    You're not calculating f(-x) correctly. Also, remember when you plug in -x for x^2, it's (-x)^2. Jhevon is right by saying the only way you're going to learn these (and math in general) is struggling through them and seeing your errors.
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  10. #10
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    Yeah, I now see how I did that one wrong, but only through that aspect. I put a positive x instead of x^2.
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  11. #11
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Monkiwrench View Post
    Yeah, I now see how I did that one wrong, but only through that aspect. I put a positive x instead of x^2.
    not only that, you put -x^2 as opposed to (-x)^2, they are not the same thing
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  12. #12
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    So how did I do on my problem? ... That you probably can't read because something screws up when I put it in [tex] script.
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  13. #13
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    Alright, I'm gonna go now. Gotta crash before I pass out right here on the keyboard. Thank you, Jhevon, for all your help and all you'll be doing for me in the future, because you're most likely gonna be the guy I'll turn to if I've got anymore questions.

    Later everybody.
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  14. #14
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Monkiwrench View Post
    So how did I do on my problem? ... That you probably can't read because something screws up when I put it in [tex] script.
    i told you how you did. fix the errors AfterShock and i told you about. and set out your problems like i showed you. it just doesn't "flow." and you never stated your conclusion as to whether it was odd or even or neither
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