## Calculus (3rd Edition)

$fog=\sqrt {x+1}$ The domain of $fog$: {x: x$\geq$-1} $gof=\sqrt x +1$ The domain of $gof$: {x: x$\geq$0}
$fog=f(g(x))=f(x+1)=\sqrt {x+1}$ Domain of g is the set of all reals and that of f is all non-negative reals. This implies that x+1 should be non-negative. $\implies\,\,$ x should be greater than or equal to -1. That is, the domain of $fog$ is the set {x: x$\geq$-1} $gof=g(f(x))=g(\sqrt x)=\sqrt x +1$. As the domain of g is the set of all real numbers, the domain of $gof$ is simply the domain of f and that is {x: x$\geq$0}