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Domain of an inverse function

  • Thread starter nokia8650
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  • #1
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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
 
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Answers and Replies

  • #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.
 
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  • #3
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The range of 4-2x would be greater than 0.
 
  • #4
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Hi, thanks, but im still confused! What would be the range of the function then?
 
  • #5
Defennder
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That would be the range of the natural logarithm, as stated earlier. Do you see why?
 
  • #6
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So the range would be any real number? Yes, i see why; it is a logarithm of any number >0, as 4-2x > 0.
 
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