Problem

Passage - 1 (Question 60 to 62): If the period of a function

f(x)

T

. Then if we find the range of function over one period then it would be the complete range of the function. If

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

and

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

where

\{.\}

denotes fractional part function then the range of

f(g(x))

is (a)

R

(b)

[0, 1]

(c)

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

(d)

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