Answer
$f(x)$ has an a discontinuity at every integer value of $x.$
These discontinuities are not removable.
Work Step by Step
Using Theorem $1.11:$
Since $f(x)=5$ is continuous for all values of x, but $g(x)=[[x]]$ is continuous for all non-integer values of $x$; $f(x)-g(x)$ is discontinuous for all integer values of x.
These discontinuities (jump) are irremovable.
