## Calculus, 10th Edition (Anton)

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, $$x=-1.$$