The domain of the function $f(x) = \sin^{–1}\left({|x|+5\over x^2+1}\right)$ is $(–\infty, –a] \cup [a, \infty)$, Then a is equal to :

(1) ${1+\sqrt{17}\over2}$

(2) ${\sqrt{17}-1\over2}$

(3) ${\sqrt{17}\over2}$

(4) ${\sqrt{17}\over2}+1$

(1) ${1+\sqrt{17}\over2}$

(2) ${\sqrt{17}-1\over2}$

(3) ${\sqrt{17}\over2}$

(4) ${\sqrt{17}\over2}+1$