How can I prove the function is convex?

Question

how can I determine if the conditioned function is convex? If so, how can I prove it?

The function is $$ f(x,y)=\frac{x^2}{y^2}+y^2,\\y\geq\sqrt{x}\quad\text {and} \quad x>0, $$ That's the question, I can't tell if it's convex.[![function figure over [0.1, 2]$\times$[0.1, 2] region,

Answer 1

The line joining two points of the domain does not lie in the domain so the domain is not convex. Consequently your function is not convex.