1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    y+y=x/x
     
  2. jcsd
  3. Nov 9, 2015 #2

    Mark44

    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)

    x=y/(1+y)
    y=x+xy

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

    Mark44

    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
    y(1+x)=x
    1+x=x/y
     
    Last edited: Nov 9, 2015
  7. Nov 9, 2015 #6

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    OK.

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

    Mark44

    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

    User Avatar
    Science Advisor
    Homework Helper

    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

    Mark44

    Staff: Mentor

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

    HallsofIvy

    User Avatar
    Staff Emeritus
    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:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted