Results 1 to 9 of 9

Math Help - What does -f(x) mean? Is it the same thing as f(-x)?

  1. #1
    Junior Member
    Joined
    Jul 2011
    Posts
    34

    What does -f(x) mean? Is it the same thing as f(-x)?

    So, In my precalc class we're learning whether or not a function is odd. And I keep on seeing this function notation -f(x) how do i evaluate it, is it just the opposite of the function? or is it just -1[f(x)]?

    And what about if i'm trying to find out if a conic section is symmetrical to the origin, for instance an equation like x^2 + y^2 = 25, how do I do this -f(x) on an equation in which y isn't separated from the rest of the variables?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1

    Re: What does -f(x) mean? Is it the same thing as f(-x)?

    Quote Originally Posted by glambeth View Post
    So, In my precalc class we're learning whether or not a function is odd. And I keep on seeing this function notation -f(x) how do i evaluate it, is it just the opposite of the function? or is it just -1[f(x)]?

    And what about if i'm trying to find out if a conic section is symmetrical to the origin, for instance an equation like x^2 + y^2 = 25, how do I do this -f(x) on an equation in which y isn't separated from the rest of the variables?

    I think this should help: Even and odd functions - Wikipedia, the free encyclopedia
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jul 2011
    Posts
    34

    Re: What does -f(x) mean? Is it the same thing as f(-x)?

    I understand most of the stuff on that aforementioned wikipedia aritcle, however, I don't understand how to evaluate -f(x) of a function. Care to elucidate that to me?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1

    Re: What does -f(x) mean? Is it the same thing as f(-x)?

    Quote Originally Posted by glambeth View Post
    I understand most of the stuff on that aforementioned wikipedia aritcle, however, I don't understand how to evaluate -f(x) of a function. Care to elucidate that to me?
    Yes.

    If f(x)=x^2+5x then -f(x)=-(x^2+5x)=-x^2-5x; if g(x)=sin(x) then -g(x)=-sin(x)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,659
    Thanks
    1616
    Awards
    1

    Re: What does -f(x) mean? Is it the same thing as f(-x)?

    Quote Originally Posted by glambeth View Post
    I understand most of the stuff on that aforementioned wikipedia aritcle, however, I don't understand how to evaluate -f(x) of a function. Care to elucidate that to me?
    Here is an example.
    Suppose that f(x)=x^4-3x^3-2x^2+x+1.
    Now -f(x)=-(x^4-3x^3-2x^2+x+1)=-x^4+3x^3+2x^2-x-1.

    Whereas,
    f(-x)=(-x)^4-3(-x)^3-2(-x)^2+(-x)+1=x^4+3x^3-2x^2-x+1.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1

    Re: What does -f(x) mean? Is it the same thing as f(-x)?

    Quote Originally Posted by glambeth View Post
    So, In my precalc class we're learning whether or not a function is odd. And I keep on seeing this function notation -f(x) how do i evaluate it, is it just the opposite of the function? or is it just -1[f(x)]?

    And what about if i'm trying to find out if a conic section is symmetrical to the origin, for instance an equation like x^2 + y^2 = 25, how do I do this -f(x) on an equation in which y isn't separated from the rest of the variables?
    x^2+y^2=25

    y^2=25-x^2

    Then, f(x)=y=\sqrt{25-x^2} or g(x)=y=-\sqrt{25-x^2}.

    -f(x)= -\sqrt{25-x^2}

    -g(x)=\sqrt{25-x^2}
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28

    Re: What does -f(x) mean? Is it the same thing as f(-x)?

    I like to say that -f(x) is f(x) reflected around the x-axis.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2

    Re: What does -f(x) mean? Is it the same thing as f(-x)?

    Quote Originally Posted by pickslides View Post
    I like to say that -f(x) is f(x) reflected around the x-axis.
    And f(-x) is f(x) reflected about the y-axis.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,392
    Thanks
    758

    Re: What does -f(x) mean? Is it the same thing as f(-x)?

    -f(x) is indeed (-1)(f(x)). f(-x) is f applied to -x.

    for example: f(x) = x^2

    f(-x) = (-x)^2 = (-x)(-x) = x^2 = f(x), this function is even.

    -f(x) = (-1)(f(x)) = (-1)(x^2) = -x^2.

    another example: g(x) = x^3.

    g(-x) = (-x)^3 = -x^3 = (-1)(x^3) = -g(x). this function is odd.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Are these asking me the same thing?
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 5th 2011, 05:10 PM
  2. Replies: 1
    Last Post: December 6th 2009, 11:00 PM
  3. is there such a thing ??
    Posted in the Calculus Forum
    Replies: 12
    Last Post: April 29th 2008, 11:42 AM
  4. Replies: 8
    Last Post: April 15th 2008, 05:43 PM

Search Tags


/mathhelpforum @mathhelpforum