# Thread: Prove that the composite g o f: X->Z is also a bijection and that

1. ## Prove that the composite g o f: X->Z is also a bijection and that

9.5 on picture. https://imgur.com/a/hwoI1oi

2. ## Re: Prove that the composite g o f: X->Z is also a bijection and that

just to be clear: to help solve this problem, we use a proposition used in the chapter. The proposition states that if we have a function f: X->Y and a function g:Y->X, they are inverses of each other if and only if g o f = Identity function of X, and f o g = Identity function of Y. I am aware how to prove this. I am not fond of the solution in the book for this problem. Or, I guess I do not understand the solution they use. here is there solution: https://imgur.com/a/SyOIWdn

In the solution, why do they omit the Identity function of Y?

3. ## Re: Prove that the composite g o f: X->Z is also a bijection and that

Found out how to solve this...from chapter 8 we had a propety that f o Identity function of x = f = identity function kf y o f.....

4. ## Re: Prove that the composite g o f: X->Z is also a bijection and that

I was wrong...sigh...can anyone help me out here.