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Math Help - Injective functions

  1. #1
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    Exclamation Injective functions

    Let f : A → B et g : B → C be 2 functions

    Show that if g ◦ f is injective, then f has to be injective
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  2. #2
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    This isn't true, take \cdot ^2:\mathbb{R}\rightarrow[0,\infty) and \sqrt{}:[0,\infty)\rightarrow [0,\infty).
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  3. #3
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    Quote Originally Posted by Focus View Post
    This isn't true, take \cdot ^2:\mathbb{R}\rightarrow[0,\infty) and \sqrt{}:[0,\infty)\rightarrow [0,\infty).
    Notice that \sqrt{} \circ \cdot^2 is not injective.

    As for the problem assume f(x)=f(y) then g(f(x))=g(f(y)) which implies x=y by the injectivity of g\circ f
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