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Annoying Calculus Problem

  1. Sep 25, 2007 #1
    1. The problem statement, all variables and given/known data
    Let F(x)=x + 1 / x

    a.) sketch graph
    b.)From the Graph, it appears that f(x) becomes 1:1 when we restrict its domain to each of the four intervals (-infinity, -1], [-1,0), (0,1] and [1, infinity). For Each of these intervals, find a formula for the inverse of f(x) restricted to the interval.


    2. Relevant equations

    Well i sketched the graph which is 2 asymptotes in the X and Y Direction in quadrant 1 and 3... but where do i go from here? i really don't understand the question... just need some help as to where i start and where i end... thank you.



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 25, 2007 #2

    EnumaElish

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    The question is, can you express x in terms of y by solving y = F(x), for each of the intervals?
     
  4. Sep 25, 2007 #3
    Yes You can solve x in terms of y...sorry i don't know what to do next
     
    Last edited: Sep 25, 2007
  5. Sep 25, 2007 #4

    EnumaElish

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    Solve x in terms of y. I will represent the solution as x = g(y), where g(y) is for you to find. Then see over which intervals (on the x axis) g is a well-defined function. (That is, make sure that g is defined over each of the four subintervals.)
     
    Last edited: Sep 25, 2007
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