let f: From A to B. let g: From B to A.

How do I prove f(g(x)) = x (indentity function) implies f is onto (surjective).

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- Nov 3rd 2009, 02:18 PMl888l888l888Surjective functions
let f: From A to B. let g: From B to A.

How do I prove f(g(x)) = x (indentity function) implies f is onto (surjective). - Nov 4th 2009, 02:23 AMHallsofIvy
- Nov 4th 2009, 06:53 AMl888l888l888
f(g(y))= y because f(g(x))=x

- Nov 4th 2009, 03:51 PMDrexel28
More explicitly (like HallsOfIvy said)

: Suppose that and are functions such that (identity mapping on Y). Prove that is surjective.**Problem**

Let . Since we know that . Therefore since . And since was arbitrary this proves surjectivity.**Proof:**