How do I determine whether they are injective or surjective f(x,y) = (|x|,|y|) and f(x,y) = (0,y)
Thank you very much
Thank you very much
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Let's give them different names:
f(x,y) = (|x|,|y|) and g(x,y) = (0,y)
For the range RxR, neither is injective since more than one value in the domain is mapped to the range. E.g., f(-1,-1) = f(-1,1) = f(1,-1) = f(1,1) = (1,1)
g(0,1) = g(π,1) = (0,1).
They are not surjective either (for the codomain RxR), since, e.g., (-1, 5) is not in the range of either.
f(x,y) = (|x|,|y|) and g(x,y) = (0,y)
For the range RxR, neither is injective since more than one value in the domain is mapped to the range. E.g., f(-1,-1) = f(-1,1) = f(1,-1) = f(1,1) = (1,1)
g(0,1) = g(π,1) = (0,1).
They are not surjective either (for the codomain RxR), since, e.g., (-1, 5) is not in the range of either.