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Does the equation x^2+y^2=100 define y as a function of x

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Answer:


x^(2) + y^(2) = 100 does not define
y as a function of
x.

Explanation:

In a function, for every valid input value
x, there should only be one unique output value
y.

For example, consider a mapping that includes both
(6,\, 8) and
(6,\, -8). This mapping isn't a function. The reason is that the input
x = 6 is mapped to more than one output values:
y = 8 and
y = (-8).

For the given equation
x^(2) + y^(2) = 100, there might be more than one possible output values
y for some input values
x. The reason is that
y^(2) = (-y)^(2).

For example, if the input value is
x = 6, then both
y = 8 and
y = (-8) (output values) would satisfy this equation:


6^(2) + 8^(2) = 100.


6^(2) + (-8)^(2) = 100.

Hence, the mapping defined with
x^(2) + y^(2) = 100 (with
x as input and
y as output) is not a function.

User Nirsky
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