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Inverse of a Function

  1. Dec 10, 2012 #1
    1. The problem statement, all variables and given/known data

    Given f(x) = x2+3x+2, what is f-1(f(x))?

    2. Relevant equations



    3. The attempt at a solution

    Algebraically, getting f-1(x) is as follows:

    y=x2+3x+2
    x=y2+3x+2
    y=+/-√(x+0.25)-1.5
    f-1(x)=+/-√(x+0.25)-1.5

    f-1(f(x))=+/-√(x2+3x+2+0.25)-1.5
    f-1(f(x))=+/-√(x+1.5)2-1.5
    f-1(f(x))=x or -x-3

    I thought f-1(f(x)) was always x. What's wrong with -x-3?
     
  2. jcsd
  3. Dec 10, 2012 #2

    Dick

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    Science Advisor
    Homework Helper

    Yes, it's always x. Your function doesn't even have an inverse, it's not 1-1. As the +/- is telling you. That's what's going wrong.
     
  4. Dec 10, 2012 #3
    So does that mean the question is faulty since the inverse is not a function?
     
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