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Homework Help: Find inverse for f(x)= x/(1+x)

  1. Nov 9, 2015 #1
    1. The problem statement, all variables and given/known data
    Show that the functions f are one-to-one and calculate the inverse function.
    2. Relevant equations
    f(x)= x/(1+x) (It is the equation I am having trouble with)

    3. The attempt at a solution
    I know the solution is y= x/(1-x) But no idea how to solve it.

    My attempt:
    x(1+y)=y or x+xy=y

  2. jcsd
  3. Nov 9, 2015 #2


    Staff: Mentor

    Start with ##y = \frac x {1 + x}##
    What's the first thing you need to do?
    I'm not sure what you did here.
  4. Nov 9, 2015 #3
    Where did you get y = x/(1+x) ?

    What i normally do is
    f(x) = x/(1+x) <=> x=f^-1(y)
    f(y) = y/(1+y) <=> y=f^-1(x)


    And now I'm stuck
  5. Nov 9, 2015 #4


    Staff: Mentor

    The above doesn't help you with this problem. All you're doing is manipulating symbols.
    In the line above, all you did was switch x and y.
    How did you get the equation above?
    Start with y = ##\frac x {1 + x}##

    For this problem DO NOT switch the variables x and y.
    DO solve for x in the equation just above. In other words, x should appear only on one side of the equation.
  6. Nov 9, 2015 #5
    Last edited: Nov 9, 2015
  7. Nov 9, 2015 #6


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    Staff Emeritus
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    Now divide both sides by x.
  8. Nov 9, 2015 #7


    Staff: Mentor

    That's the function you're trying to find the inverse of.
    Multiplying both sides of this equation by 1 + x gives you the equation just below.
    It's probably simpler to expand y(1 + x), get all terms that involve x on one side, and then isolate x.
  9. Nov 9, 2015 #8

    Ray Vickson

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    Why do you call this a "transcendental function"? It is just about as far from transcendental as you can get.
  10. Nov 9, 2015 #9


    Staff: Mentor

    I changed the title a while ago for that very reason.
  11. Nov 10, 2015 #10


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    Science Advisor

    Subtract xy from both sides: y- xy= y(1-x)= x
  12. Nov 10, 2015 #11
    Managed to solve this late yesterday.
    Thanks for trying to help.:smile:
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