surjective function-10分

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Definition of Surjective:

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Let y be a testing element belonging to B.
Let x=y3, where x should be an element of A.

As g(y3)=y, there exists an element of A such that g(x)=y.
As y is arbitrary testing element, every y can draw the above conclusion.

This satisfies the definition of surjective.

sin(x)=y

let sin^-1y=x

sin(sin^(-1)y)=y

also,but obviously,sin(x) is not surjective,
how to explain this?

2011-08-25 21:52:47 補充：
Also ,how to use the existence of inverse?

就這一條，我們可以用existence of inverse => bijective => surjective，會方便好多。