Let f(x)= cases x-3,&x<0 ^2-3x+2,&x 0 cases and

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

Problem

Let

f(x)=\begin{cases}x-3,&x<0\\x^2-3x+2,&x\geq 0\end{cases}

and

g(x)=f(|x|)+|f(x)|

. Which one of the following is correct? (a)

g(x)

is continuous

\forall x\in R

(b)

g(x)

has a removable type of isolated point discontinuity at

x=0

(c)

g(x)

has non-removable finite type of discontinuity at

x=0

and jump of discontinuity is equal to 1. (d)

g(x)

has non-removable finite type of discontinuity at

x=0

and jump of discontinuity is equal to 2.