Results 1 to 4 of 4

Math Help - determining whether this function is one to one or not

  1. #1
    Member
    Joined
    Aug 2008
    Posts
    249

    determining whether this function is one to one or not

    how do you determine whether this function is one to one or not?
    y = x^3 - 4x^2 + 2

    f(a) = f(b), a=/=b
    a^3 - 4a^2 +2 = b^3 - 4b^2 +2
    a^3 - 4a^2 = b^3 - 4b^2 (subtract 2 from both sides)
    a^3 - b^3 - 4a^2 + 4b^2 = 0
    (a - b)(a^2 + ab + b^2) - 4(a^2 - b^2) = 0
    (a - b)(a^2 + ab + b^2) - 4(a + b)(a - b) = 0
    (a - b)(a^2 + ab + b^2 - 4a - 4b) = 0

    i'm not sure on what to do next. this is where i'm stuck. what i'm supposed to do is solve for the two factors. for example the first factor results in a = b. but i need to somehow solve for the second factor so i can see whether my two solutions contradict with the statement a=/=b or not. i've been using the above method for all of my homework problems but it doesn't seem to work on this particular problem. my teacher only showed us this way of doing it. any suggestions?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,623
    Thanks
    428
    This is fairly easy if one can use calculus, but I took note that this post is in the precalculus section. I tried playing with the algebra of your attempt, but couldn't make anything break loose ... and then I noticed that f(0) = f(4).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Aug 2008
    Posts
    249
    Quote Originally Posted by skeeter View Post
    This is fairly easy if one can use calculus, but I took note that this post is in the precalculus section. I tried playing with the algebra of your attempt, but couldn't make anything break loose ... and then I noticed that f(0) = f(4).
    thanks for trying it haha. i would like to ask how you came up with
    f(0) = f(4). are those just random numbers or did you determine them somehow?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,616
    Thanks
    1579
    Awards
    1
    Quote Originally Posted by oblixps View Post
    i would like to ask how you came up with
    f(0) = f(4). are those just random numbers or did you determine them somehow?
    I do not mean to answer for Skeeter.
    However, this is a setup question.
    Consider, f(x)=x^3-ax^2+2\;,\; a\not=0 then f(0)=f(a).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. determining a profit function
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: March 25th 2011, 05:01 PM
  2. [SOLVED] Determining the countability of a set of function.
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: October 12th 2010, 09:55 AM
  3. Determining a function
    Posted in the Calculus Forum
    Replies: 4
    Last Post: June 7th 2010, 10:17 AM
  4. Determining if a function is differentiable
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 2nd 2009, 06:31 AM
  5. Determining whether a function is 1-to-1 &/or onto
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: November 18th 2008, 09:30 AM

Search Tags


/mathhelpforum @mathhelpforum