- #1
foxtrot_echo_
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Consider the mapping f: X[tex]\rightarrow[/tex]Y where f(x)=y=[tex]\sqrt{1-x^2}[/tex]
consider the co-domain Y , we can define the mapping over [-1,1] [tex]\rightarrow[/tex] [tex]\mathbb R[/tex] , ( in this case the mapping won't be onto)
and in case we define the mapping over [-1,1] [tex]\rightarrow[/tex] [0,1] (in this case mapping is onto)
(is my understanding till this point right?)
and my question is
does it make any sense to say that the domain X is the set [tex]\mathbb R[/tex] or can the mapping only be defined such that X is the set [-1,1] (or its subsets) ?
(note I am not considering case of complex numbers)
and another minor quibble :- when we plot y = [tex]\sqrt{1-x^2}[/tex] , why do we show the domain X over entire real line shouldn't we only show the line segment from [-1,1] (if it doesn't make any sense to say X is entire [tex]\mathbb R[/tex]) ?
consider the co-domain Y , we can define the mapping over [-1,1] [tex]\rightarrow[/tex] [tex]\mathbb R[/tex] , ( in this case the mapping won't be onto)
and in case we define the mapping over [-1,1] [tex]\rightarrow[/tex] [0,1] (in this case mapping is onto)
(is my understanding till this point right?)
and my question is
does it make any sense to say that the domain X is the set [tex]\mathbb R[/tex] or can the mapping only be defined such that X is the set [-1,1] (or its subsets) ?
(note I am not considering case of complex numbers)
and another minor quibble :- when we plot y = [tex]\sqrt{1-x^2}[/tex] , why do we show the domain X over entire real line shouldn't we only show the line segment from [-1,1] (if it doesn't make any sense to say X is entire [tex]\mathbb R[/tex]) ?
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