I've been struggling with the compositions and injection/surjection so I borrowed a book from my professor and I was using both books to teach myself. I've gotten considerably better at the application of the onto and one-to-one (i.e. actually composing two functions and determining whether it's onto, one-to-one, or both/neither) ... The next portion of the excercise has me a bit stumped, it's a more abstract concept which requires me to prove ....
Suppose f, g, and h are all mappings of a set A into itself.
(a) Prove that if g is onto and , then .
(b) Prove that if f is one-to-one and , then .
I've been memorizing the definitions for injection, surjection, and image as well as a few others but I'm having a really hard time visualizing these and I think that's why I'm not able to prove them. Thanks for any help you guys can provide!