Answer
(a) $0$
(b) $0$
(c) $-1$
(d) $\sqrt{15}$
(e) $\sqrt{x^2-1}$
(f) $x-1$ such that $x\geq 0$
Work Step by Step
(a)
$f(g(1))$
$f(1^2-1)$
$f(0)$
$\sqrt{0}$
$0$
(b)
$g(f(1))$
$g(\sqrt{1})$
$g(1)$
$1^2-1$
$0$
(c)
$g(f(0))$
$g(\sqrt{0})$
$g(0)$
$0^2-1$
$-1$
(d)
$f(g(-4))$
$f((-4)^2-1)$
$f(15)$
$\sqrt{15}$
(e)
$f(g(x))$
$f(x^2-1)$
$\sqrt{x^2-1}$
(f)
$g(f(x))$
$g(\sqrt{x})$
$\sqrt{x}^2-1$
$x-1$
Domain: $x\geq0$ because the expression under the square root must be greater than or equal to 0
