The function defined by ( denotes the greatest integer function) satisfies

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

Problem

The function defined by

f(x)=(-1)^{[x^3]}

(

[\cdot]

denotes the greatest integer function) satisfies (a) discontinuous for

x=n^{1/3}

, where

n

is any integer (b)

f(3/2)=1

(c)

f'(x)=1

for

-1<x<1

(d) none of these