Limits — a difference of square roots at infinity

For a non-negative real number $a$, let $\sqrt{a}$ denote its non-negative square-root. Consider the function $f:\mathbb{R}\to\mathbb{R}$ given by

$$f(x)=x\left(\sqrt{x^2+3}-\sqrt{x^2+2}\right).$$

Which of the following statements is true?