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Math Help - injective functions

  1. #1
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    Question injective functions

    Prove that if f:A→B and g:B→C and if g◦f is injective,then f must be injective.
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  2. #2
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    Quote Originally Posted by hebby View Post
    Prove that if f:A→B and g:B→C and if g◦f is injective,then f must be injective.

    f(a)=f(a')\Longrightarrow gf(a)=gf(a') , but gf is injective so...

    Tonio
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  3. #3
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    f must be injective ? thats it?
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    Quote Originally Posted by hebby View Post
    f must be injective ? thats it?

    errr....yes, of course, but you still need a little more work to do. Think.

    Tonio
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  5. #5
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    Question

    well i wrote Suppose f(x) = f(y). Then g(f(x)) = g(f(y)), so, since g ◦ f is 11, it follows that x = y. Therefore, f is 11....is this ok?
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  6. #6
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    Quote Originally Posted by hebby View Post
    well i wrote Suppose f(x) = f(y). Then g(f(x)) = g(f(y)), so, since g ◦ f is 11, it follows that x = y. Therefore, f is 11....is this ok?

    Very good.

    Tonio
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