If (where denotes the greatest integer function) and

MATHEMATICS · Single correct · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

f(x)=\left\lfloor x^{-2}\left\lfloor x^2\right\rfloor\right\rfloor

(where

\lfloor\cdot\rfloor

denotes the greatest integer function) and

x\neq 0

, which statement is incorrect? (1)

f(x)

is continuous everywhere (2)

f(x)

is discontinuous at

x = \sqrt{2}

(3)

f(x)

is non-differentiable at

x = 1

(4)

f(x)

is discontinuous at infinitely many points