Answer
$$
f(x)=\left|4-\frac{8}{x^{4}+x}\right|
$$
values of $x$, at which $f $ is not continuous are $x = 0$, $ x = -1$
Work Step by Step
$$
f(x)=\left|4-\frac{8}{x^{4}+x}\right|
$$
suppose
$$
f(x)=|g(x)-h(x)|
$$
such that
$$g(x)= 4, \quad \quad h(x)=\frac{8}{x^{4}+x} $$
Solving the equation
$$
x^{4}+x=x(x^{3}+1)=0
$$
yields discontinuities at $x = 0$ and at $ x = -1$.
Therefore the function
$$
\frac{8}{x^{4}+x}
$$
is continuous for all real numbers $x$ except $x = 0$ , $ x = -1$
Thus the function
$$
f(x)=\left|4-\frac{8}{x^{4}+x}\right|
$$
is continuous for all real numbers $x$ except $x = 0 $, $x = -1$.
Finally,
values of $x$, at which $f $ is not continuous are $x = 0$, $ x = -1$
