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Grade 12 Math (inverse of functions)

  1. Sep 16, 2015 #1
    • Member warned about posting homework in a technical section
    f(x)=[((x-1)/(x+1))+((x-1)/(x+1))]1/2

    What is F-1(x)

    No matter what I try I am unable to isolate for y after switching x's with y's. Any ideas?
     
  2. jcsd
  3. Sep 16, 2015 #2

    Mark44

    Staff: Mentor

    The innermost expression is ##\frac{x - 1}{x + 1} + \frac{x - 1}{x + 1}##, which can be simplified. Is that what you meant to write?
    BTW, this looks like a homework problem, so I'm moving this thread.
     
  4. Sep 17, 2015 #3

    RUber

    User Avatar
    Homework Helper

    This is a pretty common problem. I'll work on a similar one as an example.
    ##y = \sqrt{ \frac{x-1}{x+1} } ##
    ##y^2 = \frac{x-1}{x+1},\, y\geq 0##
    ## y^2 = \frac{x+1}{x+1}-\frac{2}{x+1}##
    ## y^2-1 = -\frac{2}{x+1}##
    ##x+1 = -\frac{2}{y^2-1}##
    ##x= -\frac{2}{y^2-1}-1=-\frac{2}{y^2-1}-\frac{y^2-1}{y^2-1}=-\frac{y^2+1}{y^2-1}##
     
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