Chapter 0 - Before Calculus - 0.2 New Functions From Old - Exercises Set 0.2 - Page 25: 52

The solution of the equation $f(g(x))=0$ is $$x=-1.$$ The solution of the equation $g(f(x))=0$ is $$x=-1.$$

According to the table, since $f(x)=0$ for $x=1$, the solutions of $f(g(x))=0$ are $x$ for which $g(x)=1$, that is, $$x=-1.$$ According to the table, since $g(x)=0$ for $x=-2$, the solutions of $g(f(x))=0$ are $x$ for which $f(x)=-2$, that is, $$x=-1.$$