
#1
Apr612, 01:23 PM

P: 200

Given a function f(x) f:A > B, can the choice of codomain affect whether or not the function is surjective? For instance, f(x) = exp(x), f:R > R is an injection but not surjection. However, assuming we can vary the codomain, and lets make it f: R > (0, inf), f(x) is now bijection. Is this correct?




#2
Apr612, 02:16 PM

P: 771

Yes. The codomain pretty much determines by itself whether or not the function is surjective.




#3
Apr612, 02:24 PM

P: 200

Got it. Thanks.




#4
Apr612, 04:23 PM

P: 771

Function Codomain! 



#5
Apr612, 06:07 PM

P: 200

But there's no rule which restricts the specification of the codomain based on the mapping rule itself as long as the range is a subset of the codomain. For instance, f(x) = sin(x) can be specified as:
f: R > R f: R > [2, 2) f: R > [1, 1] but not as f: R > [0, 4] 


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