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.

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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.

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Answer 1 · 2018-07-25T00:48:39

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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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

Explanation:

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