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Inverse of a function

  1. Sep 29, 2012 #1
    1. The problem statement, all variables and given/known data

    I need to find the inverse of y=x+√(x^2-1)

    2. Relevant equations



    3. The attempt at a solution

    I know it's undefined from x=-1 and x=1 so there must be two different inverse functions on two different intervals. I don't know how to find them though.
     
  2. jcsd
  3. Sep 29, 2012 #2

    HallsofIvy

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    You find the inverse pretty much the way you find any inverse:
    Given [itex]y= x+ \sqrt{x^2- 1}[/itex], solve for x. Since there is a square root, we will want to square, and, in order not to get another square root in the "cross term" we want it by itself: [itex]y- x= \sqrt{x^2- 1}[/itex]. Now square that and solve for x.

    Note the while x cannot be between -1 and 1, y can go to 0.
     
  4. Sep 29, 2012 #3

    SammyS

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    Let's call the function you are given, f, so that
    [itex]f(x)=x+\sqrt{x^2-1}\ .[/itex]​

    Following HallsofIvy's suggestion you will find:
    [itex]x=g(y)\ .[/itex]​
    For the function, g, to be the inverse of function, f, it must also be true that g is the inverse of f. However, the domain of g will need to be restricted (to the range of f) so that g is a 1 to 1 function.
     
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