Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

Is $x^{2} - y^{2} = 7$ $x^2 - y^2 = 7$ a function?

1 Answer

Jul 8, 2015

$x^{2} - y^{2} = 7$ $x^2-y^2=7$ is not a function

Explanation:

$x^{2} - y^{2} = 7$ $x^2-y^2=7$
could be rearranged as
$XXXX$ $color(white)("XXXX")$ $y^{2} = x^{2} - 7$ $y^2 = x^2-7$

So
$XXXX$ $color(white)("XXXX")$ $y = \pm \sqrt{x^{2} - 7}$ $y = +-sqrt(x^2-7)$

That is for $x^{2} > 7$ $x^2 > 7$ there is more than one value for $y$ $y$
which is contrary to the requirement for an equation to be a function.

Related questions

See all questions in Function Notation

Impact of this question

4399 views around the world

You can reuse this answer
Creative Commons License