Limits Continuity And Differentiability Question 7

Question: The function f(x)=|2 sgn 2x|+2 has

Options:

A) jump discontinuity

B) removal discontinuity

C) infinite discontinuity

D) no discontinuity at x=0

Show Answer

Answer:

Correct Answer: A

Solution:

f(x)=|2 sgn 2x|+2 $ = \begin{matrix} 4,x>0 \\ 2,x=0 \\ 0,x<0 \\ \end{matrix} . $

Thus, f(x) has non-removable discontinuity at x=0