I have two functions: $f(x) = x^{2}-3|x-1|$ and $g(x)=2|x-2|$.
I need to find the sum of all integer solutions for the following inequality: $g[f(x)]\leq 2$
I have two functions: $f(x) = x^{2}-3|x-1|$ and $g(x)=2|x-2|$.
I need to find the sum of all integer solutions for the following inequality: $g[f(x)]\leq 2$
Presumably by "roots" you mean solutions. (The term "roots" is usually reserved for solutions of equations.)
The inequality is fulfilled if $|f(x)-2|\le1$. Since $f(x)$ takes integer values at the integers, that means $f(x)\in\{1,2,3\}$. Substituting the integers from $-5$ to $5$ shows that the only solution is $x=3$.