Let , where and denotes the greatest integer function. If is an odd function, then…

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

Problem

Let

f:[-10,10]\to\mathbb{R}

, where

f(x)=\sin x+\left\lfloor\frac{x^2}{a}\right\rfloor

and

\lfloor\cdot\rfloor

denotes the greatest integer function. If

f

is an odd function, then the set of values of parameter

a

is (a)

(-10,10)\setminus\{0\}

(b)

(0,10)

(c)

[100,\infty)

(d)

(100,\infty)