Solve composition of functions and isomorphisms

Reference no: EM13124462

Composition of Functions and Isomorphisms

I can't prove the following statements about functions f:A->B and g:B->C

1. If gof is one-to-one then so is f.

2. If gof is onto then so is g.

Furthermore I don't know how to show that f: A->B is an isomorphism of sets if and only if there is a function g: B->A such that gof=1A and fog=1B.

Here fog and gof are compossitions of functions f and g respectively.

fog=f(g(x)) and gof=g(f(x)) and 1A denotes identity ofn A and 1B denotes identity on B

Reference no: EM13124462

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