Chapter 10 - Section 10.3 - Limits and Continuity: Algebraic Viewpoint - Exercises - Page 719: 80

$h$ is discontinuous at $x=1.$

$x=1$ is of interest to us, as it is the only value where $h(x)$ can have a discontinuity. We have: $h(1)=1$ Te right-sided limit:$\qquad \displaystyle \lim_{x\rightarrow 1+}h(x)=1+2=3$ which does not equal $h(1)$, so: $h$ is discontinuous at $x=1.$