injective functions

**hebby** · November 21st 2009, 10:16 AM

Prove that if f:A→B and g:B→C and if g◦f is injective,then f must be injective.

**tonio** · November 21st 2009, 10:25 AM

Originally Posted by hebby

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

**hebby** · November 21st 2009, 10:27 AM

f must be injective ? thats it?

**tonio** · November 21st 2009, 10:39 AM

Originally Posted by hebby

f must be injective ? thats it?

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

Tonio

**hebby** · November 21st 2009, 10:48 AM

well i wrote Suppose f(x) = f(y). Then g(f(x)) = g(f(y)), so, since g ◦ f is 1–1, it follows that x = y. Therefore, f is 1–1....is this ok?

**tonio** · November 21st 2009, 11:34 AM

Originally Posted by hebby

well i wrote Suppose f(x) = f(y). Then g(f(x)) = g(f(y)), so, since g ◦ f is 1–1, it follows that x = y. Therefore, f is 1–1....is this ok?

Very good.

Tonio

Thread: injective functions