Asymptotically Equal Real Functions/Examples/x^2+1 and x^2

Example of Asymptotically Equal Real Functions
Let $f: \R \to \R$ be the real function defined as:
 * $\forall x \in \R: \map f x = x^2 + 1$

Let $g: \R \to \R$ be the real function defined as:
 * $\forall x \in \R: \map g x = x^2$

Then:
 * $f \sim g$

as $x \to +\infty$.