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Finding the domain of the inverse function

  1. Jul 11, 2010 #1
    1. The problem statement, all variables and given/known data

    Let f(x)=e^(-x)-x ,, x belongs to R

    Find the domain of f inverse

    2. Relevant equations

    Domain of f inverse = range of f

    3. The attempt at a solution

    we have :

    -inf < x < inf
    -inf < -x < inf .... (1)
    0 < e^(-x) < inf .... (2)

    By adding (1) and (2) :

    -inf < e^(-x) - x < inf

    So domain of f = R = range of f inverse.

    Is this correct?

    Can I add the inequalities together?
  2. jcsd
  3. Jul 11, 2010 #2
    Ignore my last post. I read the function wrong. Yep, the domain of the inverse is all real numbers.
  4. Jul 11, 2010 #3
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