1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Inverse of a function

  1. Feb 7, 2010 #1
    1. The problem statement, all variables and given/known data

    f(-1,+1) -> R is given by f(x) = x/(1 - |x|)

    Find the inverse of f.

    Are f and the inverse of f continuous?

    2. Relevant equations



    3. The attempt at a solution

    I have shown that f is 1-1.
    f((-1,+1)) -> (-[tex]\infty[/tex], +[tex]\infty[/tex])

    Let y = f-1(x), so f(y) = x

    y/ (1- |y|) = x
    y = x(1- |y|)

    If y = 0 x = 0
    If y> 0 y =x(1-y), so y = x/(1+x)
    If y< 0 y =x(1+y), so y = x/(1-x)

    Can I say if y<0 then x <0 and if y >0 then x >0?
    Then y=x/(1+|x|)

    Would the domain of the inverse be (-[tex]\infty[/tex],+[tex]\infty[/tex])?

    If this is so, f and the inverse of f are continuous as I know f(x) =x, f(x) = 1, f(x) = |x| are continuous and if f and g are continuous then so are |f|, f+g, f-g, and f/g.
     
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted