Let . Which statement correctly describes the set of real numbers on which is…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

g(x)=\ln|\sin(2x)|

. Which statement correctly describes the set of real numbers on which

g

is continuous? (a)

g

is continuous for all

x

such that

x\neq n\pi

, where

n\in\mathbb{Z}

. (b)

g

is continuous on every interval

(n\pi,(n+1)\pi)

n\in\mathbb{Z}

(i.e. wherever

\sin(2x)>0

). (c)

g

is continuous for all

x\in\mathbb{R}

with

x\neq\dfrac{n\pi}{2}

n\in\mathbb{Z}

; that is, on every open interval between consecutive multiples of

\dfrac{\pi}{2}

. (d)

g

is continuous for all real numbers because the absolute value guarantees the argument of the

\ln

is non-negative.