The range of the function

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

f(x) = \sin^{-1} \left[ x^2 + \frac{1}{2} \right] + \cos^{-1} \left[ x^2 - \frac{1}{2} \right]

, is (Note:

[k]

denotes greatest integer function less than or equal to

k

) (a)

\{\frac{\pi}{2}, \pi\}

(b)

\{\pi\}

(c)

\{\frac{\pi}{2}\}

(d)

\{\frac{\pi}{4}, \frac{\pi}{2}\}