Is it true that if g is one-to-one then f o g must be one-to-one? Give a proof or a counterexample.

1 Answer
R. Nguyen
Jul 25, 2018

It is not true in general that if #g# is one-to-one then #f \circ g# must be one-to-one.

Explanation:

This is not true in general.

Notice that the identity function #g(x)=x# is a one-to-one function. If #f(x)# is any function that is not one-to-one, #f(g(x)) = f(x)# and is therefore also not one-to-one.

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