How to decide whether the relation 7x2+y2=1 defines a function?

algartaim6jf

algartaim6jf

Answered

2023-01-01

How to decide whether the relation 7x2+y2=1 defines a function?

Answer & Explanation

Giaj5sf

Giaj5sf

Expert

2023-01-02Added 8 answers

Simply put, a function is a rule that specifies how inputs and outputs must relate to one another.
For example, f(x)=y=sin(x) means that the rule is that, for any input x, the output will be the sine of that input.
In your case, if we solve the expression for y in order to highlight this ""rule"", we havey2=17x2y=±17x2
That ± sign means that, given a certain input x, the output can be either 17x2 or 17x2.
This is not a function because it is not true that each input results in a single and unique output.

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