Prove that if g and f are 1-1, then so is g o f. And prove that if g and f are onto, then so is g o f.

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- Apr 17th 2011, 10:22 AMandirc5192Compositions
Prove that if g and f are 1-1, then so is g o f. And prove that if g and f are onto, then so is g o f.

- Apr 17th 2011, 10:27 AMPlato
- Apr 17th 2011, 10:51 AMandirc5192
Oh geez yeah sorry about that. I understand that, by definition, g: A-->B is one to one if and only if w,x are in A where w is not equal to x and g(w)=g(x) implies that w=x, and the same thing for f:C-->D where y,z are in C. However i'm not sure how to connect the two through a composition.

- Apr 17th 2011, 11:44 AMPlato
If $\displaystyle f:A\to B$ and $\displaystyle g:B\to C$ what does $\displaystyle g\circ f(x)$ mean?

If $\displaystyle g\circ f$(y)=$\displaystyle g\circ f(x)$ show $\displaystyle y=x$