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Finding inverse functions when there is X^2+x

  1. Oct 11, 2013 #1
    1. The problem statement, all variables and given/known data

    f(x)= 2x + x^2

    2. Relevant equations



    3. The attempt at a solution

    I don't know how to make x the subject
     
  2. jcsd
  3. Oct 11, 2013 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You need to solve for x in the equation x^2 + 2x = y. This is a simple quadratic equation.
     
  4. Oct 11, 2013 #3
    Okay thank you!

    I've got it:

    X^2 +2x = y

    add one so you get a quadratic that has a "squared"

    x^2 +2x +1 = y + 1

    solve quadratic:

    (x+1)^2 = y + 1

    x = (y+1)^-1/2 -1

    f-1(x) = (x+1)^-1/2 -1

    :)
     
    Last edited: Oct 11, 2013
  5. Oct 11, 2013 #4

    Mark44

    Staff: Mentor

    No.
    Starting from two lines above, you want to solve for x.
    When you do this, don't forget that you need ± in there somewhere.
    Note that the equation y = x2 + 2x does not give y as a 1-to-1 function of x, so there is no inverse function, unless you place restrictions on the domain.
     
  6. Oct 12, 2013 #5
    You have raised to the power -1/2. Where did the negative sign come from?
     
  7. Oct 12, 2013 #6
    Sorry, mistake when I was typing! Thank you for pointing it out
     
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