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.
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-> 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
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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(52776) (Show Source):
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.
