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Domain of an inverse function

  1. Jun 5, 2008 #1
    The function f is defined by f(x) = ln(4 - 2x), x<2, and x is a real number

    write down the domain of the inverse.
    I know that the domain of the inverse is the range of the function, but I am puzzled as to what that would be! Would it just be any real number?

    Thanks
     
    Last edited: Jun 5, 2008
  2. jcsd
  3. Jun 5, 2008 #2

    Defennder

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    The range of the natural logarithm is -infinity to infinity. That means to say that that would be the range of that function if the range of 4-2x where x<2 is also just any real number. What is the range of 4-2x where x<2?

    EDIT: I just realised that the range of 4-2x where x<2 is restricted to positive real numbers.
     
    Last edited: Jun 5, 2008
  4. Jun 5, 2008 #3
    The range of 4-2x would be greater than 0.
     
  5. Jun 5, 2008 #4
    Hi, thanks, but im still confused! What would be the range of the function then?
     
  6. Jun 5, 2008 #5

    Defennder

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    That would be the range of the natural logarithm, as stated earlier. Do you see why?
     
  7. Jun 5, 2008 #6
    So the range would be any real number? Yes, i see why; it is a logarithm of any number >0, as 4-2x > 0.
     
    Last edited: Jun 5, 2008
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