"How to decide whether the relation 7x2+y2=1 defines..." was answered by our experts

algartaim6jf

Answered question

2023-01-01

How to decide whether the relation

7 x^{2} + y^{2} = 1

defines a function?

Giaj5sf

Beginner2023-01-02Added 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 have

y^{2} = 1 - 7 x^{2} \Leftrightarrow y = \pm \sqrt{1 - 7 x^{2}}

That

\pm

sign means that, given a certain input

x

, the output can be either

\sqrt{1 - 7 x^{2}}

- \sqrt{1 - 7 x^{2}}

.
This is not a function because it is not true that each input results in a single and unique output.

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