If and , where denotes the fractional-part function, then the range of…

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

Problem

f(x)=\dfrac{1}{x^2+1}

and

g(x)=\sin(\pi x)+8\left\{\dfrac{x}{2}\right\}

, where

\{\cdot\}

denotes the fractional-part function, then the range of

f(g(x))

is (a)

\mathbb{R}

(b)

[0,1]

(c)

\left(\dfrac{1}{65},1\right]

(d)

\left[\dfrac{1}{65},1\right]