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Math Help - f(x) vs. f(-x) vs. -f(x)

  1. #1
    Junior Member jonnygill's Avatar
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    f(x) vs. f(-x) vs. -f(x)

    Hello!

    Could someone elaborate on what the difference is between f(x), f(-x), and -f(x)

    Lets use the equation...

    f(x)=5x^3

    so if x=3 then f(x)=(5)(27)=135

    and if x=-3 then f(x)=(5)(-27)=-135

    what is -f(x) in this scenario? (when x=3)

    is it simply -f(x)=-(5x^3) or -f(x)=-(5\cdot27) ?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by jonnygill View Post
    Hello!

    Could someone elaborate on what the difference is between f(x), f(-x), and -f(x)

    Lets use the equation...

    f(x)=5x^3

    so if x=3 then f(x)=(5)(27)=135

    and if x=-3 then f(x)=(5)(-27)=-135

    what is -f(x) in this scenario? (when x=3)

    is it simply -f(x)=-(5x^3) or -f(x)=-(5\cdot27) ?
    You have it right.

    -Dan
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  3. #3
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    e^(i*pi)'s Avatar
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    -f(x) = -1 \cdot f(x)

    If you're graphing it will be a reflection of f(x) in the x-axis.

    In your case you have -f(x) = -(5x^3) and hence [/tex]-f(3) = -(5 \cdot 27)[/tex]

    In other words yes
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  4. #4
    MHF Contributor

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    For this particular function, f(x)= 5x^3 because it involves only an odd power of x (and so is an "odd" function), f(-x) happens to be the same as -f(x). For example, f(-2)= 5(-2)(-2)(-2)= 5(4)(-2)= -40 while -f(2)= -(5)(2)(2)(2)= -5(4)(2)= -40.

    However, if the function were 5x^2, involving x only to an even power (and so an "even" function), we would have f(-x)= f(x). For example, f(-2)= 5(-2)(-2)= 20 which is equal to f(2)= 5(2)(2)= 20.

    But most functions are neither "even" nor "odd". For example if f(x)= x+ 2, then f(-x)= -x+ 2 is not equal to either -f(x) nor f(x). For example, f(-2)= -2+ 2= 0 while f(2)= 2+ 2= 4.
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