If f(x)={|x|−3,x<1|x−2|+a,x≥1 and g(x)={2−|x|,x<2sgn(x)−b,x≥2, where sgn(x) denotes the signum function. If h(x)=f(x)+g(x) is discontinuous at exactly one point, then which of the following values of a and b are possible?

If f(x)={|x|−3,x<1|x−2|+a,x≥1 and g(x)={2−|x|,x<2sgn(x)−b,x

1.	If f(x)={\|x\|−3,x<1\|x−2\|+a,x≥1 and g(x)={2−\|x\|,x<2sgn(x)−b,x≥2, where sgn(x) denotes the signum function. If h(x)=f(x)+g(x) is discontinuous at exactly one point, then which of the following values of a and b are possible?
Answer» If $f (x) = {\begin{matrix} \| x \| - 3, & x < 1 \| x - 2 \| + a, & x \geq 1 \end{matrix}$ and $g (x) = {\begin{matrix} 2 - \| x \|, & x < 2 sgn (x) - b, & x \geq 2 \end{matrix}$ , where $sgn (x)$ denotes the signum function. If $h (x) = f (x) + g (x)$ is discontinuous at exactly one point, then which of the following values of $a$ and $b$ are possible?