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Solve equation |f^-1(x)|= 1+f^-1(x)

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  1. Oct 16, 2017 #1
    1. The problem statement, all variables and given/known data
    f(x) = (2x-3)/(x-1)
    Solve the equation |f^-1(x)|= 1+f^-1(x)

    2. Relevant equations
    I'm pretty sure f^1(x) = (-3+x)/(x-2)

    3. The attempt at a solution
    I am not sure what solve means. Do i need to plug in values?
     
  2. jcsd
  3. Oct 16, 2017 #2

    Mark44

    Staff: Mentor

    No, that wouldn't be very productive unless you just happened to pick a value that works.

    I believe the problem is asking you to find the value of x that makes the equation a true statement.
    Also, yes, the inverse is ##f^{-1}(x) = \frac {x - 3} {x - 2}##
    Replace ##f^{-1}(x)## by this expression in the equation you're given and get x all by itself.
     
  4. Oct 16, 2017 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Make life easier for yourself by letting ##f^{-1}(x) = y##, so your equation is ##|y| = 1 + y##. First figure out the value of ##y##, then figure out what must be ##x## to give you ##f^{-1}(x) = y##.
     
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