SOLUTION: 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 stat

Question 1170264: 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?
Answer by ikleyn(52779) (Show Source): You can put this solution on YOUR website!
.

It is TRUE.

Under the given condition, we can define the function g on the set of the images  {b | b = f(a), a belongs to A}  in a way


    g(b) = a,   if  f(a) = b.


This function is defined correctly on this set and is the inverse function to f.

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