If g(f(x) is injective I need to determine if f is injective. If it is false, I need to give a counterexample.

I was told that using arrow diagrams helps.

Can some one help me get started?

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- Nov 9th 2008, 07:02 PMkathrynmathg(f(x) is injective, is f injective?
If g(f(x) is injective I need to determine if f is injective. If it is false, I need to give a counterexample.

I was told that using arrow diagrams helps.

Can some one help me get started? - Nov 9th 2008, 07:17 PMkathrynmath
I know g doesn't have to be injective.

- Nov 9th 2008, 07:20 PMkathrynmath
I'm think that it does but I am unsure of how to prove this.

- Nov 9th 2008, 07:36 PMkathrynmath
So g(f(x)) is 1-1, so g(f( =g(f( . Then this implies f( =f( .

Where do I go from here? Would that last statement prove that ? therefore, f is one to one? - Nov 9th 2008, 07:56 PMJhevon
- Nov 9th 2008, 07:59 PMkathrynmath
- Nov 9th 2008, 08:01 PMJhevon
- Nov 9th 2008, 08:05 PMkathrynmath
- Nov 9th 2008, 08:08 PMJhevon
- Nov 9th 2008, 08:10 PMkathrynmath
- Nov 9th 2008, 08:17 PMJhevon
- Nov 9th 2008, 08:23 PMkathrynmath