Question

If $f\left(x\right)=\{\begin{array}{cc}|x|-3,& x<1\\ |x-2|+a,& x\ge 1\end{array}$ and $g\left(x\right)=\{\begin{array}{cc}2-|x|,& x<2\\ sgn\left(x\right)-b,& x\ge 2\end{array}$ and $h\left(x\right)=f\left(x\right)+g\left(x\right)$ is discontinuous at exactly one point, then which of the following values of a and b are possible.

• A. $a=-3,b=0$
• B. $a=2,b=1$
• C. $a=2,b=0$
• D. $a=-3,b=1$

Answer 1

Answer: (A), (B)

The correct options are
A $a=-3,b=0$
B $a=2,b=1$