Question

does this equation define y as a function of x:
x^2y+y=1

Answer 1

\[x^2y+y=1~~\iff~~y(x^2+1)=1~~\iff~~y=\frac{1}{x^2+1}\]

Answer 2

so is that yes?

Answer 3

Yep, if you can express \(y\) explicitly in terms of \(x\) only, then you've got yourself a function.

Answer 4

okay. how did you get \[y(x^2+1)=1\]

Answer 5

@SithsAndGiggles

Answer 6

Factor out the \(y\).

Answer 7

okay thank you!

Answer 8

you're welcome

Answer 9

what about \[x=y^3\]