Question 1207313
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State whether or not the given equations determines y as a function of x
(1) X+Y=1
(2) X^2 + y^2=1
(3) Y^2=X^2
(4) Y=√x
(5) Y=+-√X
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(1)  From x + y = 1, we have an equivalent equation

         y = 1-x.

    It determines "y" by an unique way via x.  So, (1) determines "y" as a function of x.



(2)  From {{{x^2}}} + {{{y^2}}} = 1, we have an equivalent expression

         y = +/- {{{sqrt(1-x^2)}}}.

    It determines two values of "y" for each value of x.  So, (2) does not determine "y" as a function of x.



(3)  From {{{y^2}}} = {{{x^2}}}, we have an equivalent expression

         y = +/- |x|.

    It determines two values of "y" for each value of x.  So, (3) does not determine "y" as a function of x.



(4)  y = {{{sqrt(x)}}}  determines a unique value of "y" for each positive value of x.  

    So, (4) determines "y" as a function of x.



(5)  y = +/- {{{sqrt(x)}}}  determines two value of "y" for each positive value of x.  

    So, (5) does not determine "y" as a function of x.
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Solved.


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