Question

Function $f\left(x\right)=|x-2|-2|x-4|$ is discontinuous at-

• A. $x=2,4$
• B. $x=2$
• C. No where
• D. Except $x=2,4$

Answer 1

Answer: (C)

No where

$f\left(x\right)=\{\begin{array}{c}x-6;x<2\\ 3x-10;2\le x\le 4\\ -x+6;x>4\end{array}$
Clearly $f\left(x\right)$ is continuous at $x=2$ and $4$
So, $f\left(x\right)$ is continuous at everywhere.