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Conjecture: If $g(x)$ is injective, and $g(f(x))$ is injective, then $f(x)$ is injective

How can I prove that conjecture formally?

Thanks!

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    I think you should specify domains and codomains of f and g. – 2012-12-15

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Let $f(a)=f(b)$. Hence $g(f(a))=g(f(b))$. Since $gf$ is injective. Therefore $a=b$

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    sorry then I don't understand why since g∘f is injective, a=b. – 2012-12-15