# Compositions

• Apr 17th 2011, 10:22 AM
andirc5192
Compositions
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 AM
Plato
Quote:

Originally Posted by andirc5192
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.

Please either post some of your own work on these problems or explain what you do not understand about the question.
• Apr 17th 2011, 10:51 AM
andirc5192
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 AM
Plato
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 $\displaystyle y=x$