Inverse functions

  • Thread starter jgens
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  • #1
jgens
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Does anyone know of an existing methodology for determining and proving whether or not a function has an inverse?

Thanks.
 

Answers and Replies

  • #2
nicksauce
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How about by determining if the function is a bijection? Or am I missing something here?
 
  • #3
HallsofIvy
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The "horizontal line test". How many times does any horizontal line cross the graph of the function? Which is the same as "determining if the function is a bijection"!
 
  • #4
jgens
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Thank you very much. Just a brief follow up question: Suppose a function is invertable but the inverse has no representation in terms of elementary functions (I'm including trigonometric and logarithmic functions in this category) - I think f(x) = x + sin(x) would meet this criterion - is there a general method for proving that the function does not have an inverse expressable in terms of elementary functions?

Sorry if that doesn't make sense.
 

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