Use algebraic means to show that x^2 + y^2 = 8 is not a function. Explain your process.

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22-10-2020
Mathematics

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Use algebraic means to show that x^2 + y^2 = 8 is not a function. Explain your process.

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FelisFelis FelisFelis · Answer 1 · 2020-10-22T20:33:05+02:00

Answer:

For a single value of x function has more than one corresponding value of y which satisfies the equation.

Step-by-step explanation:

Function: A relationship between a set of inputs and a set of possible outputs, where exactly one output is associated with each input.

It means for an equation to represent a function any single value of x there should be only one corresponding value of y which satisfies the equation.

Now consider the given equation.

[tex]x^2 + y^2 = 8[/tex]

If we put x=0 then we get two value of y i.e [tex]\sqrt8[/tex] and [tex]-\sqrt8[/tex] which satisfy the equation and therefore the equation is not a function.