$f(x,y) = \frac{x^4}{x^2+1} + |y| $
I want to see if the given function is coercive or not.
My questions is that I'm stuck on how to transform the function into $(x^2+y^2)$ form. I need to convert into that form to show that $f(x,y) \to \infty$ as $\|(x,y) \| \to \infty$.
Any hints are appreciated! Thank you!
EDIT
Although I didn't find what L is yet (copper.hat suggested this idea) but based on copper.hat's hint I got an idea that $\frac{x^4}{1+x^2}$ goes infinity as $x$ goes infinity. Likewise, $|y|$ goes infinity as $y$ goes infinity. Then if $\sqrt(x^2 + y^2)$ goes infinity, I can say that the given function also does because either $x$ or $y$ should increase for $\sqrt(x^2 + y^2)$ to be infinity, which implies that $f(x,y)$ goes infinity because either term $\frac{x^4}{x^2+1}$ or $|y|$ will go infinity.
Is this logic reasonable?