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Consider the following statement: Let  f be a function, such that for all  a and b  in the domain of f, f(a)=f(b) implies a=b.  Then the function  f has an inverse.

Is this statement true or false? 

Thank you so much!

 Nov 20, 2020
 #1
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This statement is false.  You can look at counter-examples such as f(x) = x^2 and f(x) = x^4.

 Dec 12, 2020

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