How would I interpret this function notation?

Question

$y=f(x)\Leftrightarrow x^2 y+y=7$

How do I go about even reading this, let alone solving this?

I also have to find the domain of "$f$"

Answer 1

"$y$ equals $f(x)$ if and only if $x^2y+y=7$"

That doesn't really tell you anything though. Are you supposed to isolate $y$ in the right-hand side above? If so, then you would have $y(x^2+1)=7$ which you could then write as $y=\frac{7}{x^2+1}$, and since $x^2$ is never negative (and particularly never $-1$), you can say that the domain is all of the real numbers. But this assumes whatever instructional source you are using intends you to read $y$ and $f(x)$ as the same symbolism. Regardless, it's sloppy wording/phraseology, and I don't fault you for your confusion. What I outlined above is the only thing I can think of that makes marginal sense.