## Attaining a maximum

The function $$f\colon \space \mathbb R^2 \to \mathbb R$$ is defined as $f(x, y) = \frac{1}{x^2 + y^2 + (x\cos(y) - 2x - 3e^y)^2 + 2}.$
Prove that $$f$$ attains its maximum value on $$\mathbb R$$.