Cho hàm số \(f\left( x \right) = \sqrt {{x^2} - {a^2}x + 1}  - x - 1\), (với \(a\) là tham số).

A. \(\mathop {\lim }\limits_{x \to  + \infty } f\left( x \right) = 1 - \frac{{{a^2}}}{2}.\)

B. \(\mathop {\lim }\limits_{x \to  + \infty } f\left( x \right) = \frac{{{a^2}}}{2} - 1.\)

C. \(\mathop {\lim }\limits_{x \to  + \infty } f\left( x \right) =  - \frac{{{a^2}}}{2} - 1.\)

D. \(\mathop {\lim }\limits_{x \to  + \infty } f\left( x \right) = \frac{{{a^2}}}{2} + 1.\)