Answer
a) $f\circ g = x+2$
Domain: $\{x|x\geq2 \}$
b) $g\circ f =\sqrt{x^2+2}$
Domain: $\{x|x\geq2 \}$
c) $f\circ f = x^4+8x^2+20$
Domain: $\{x|\Re \}$
d) $g\circ g =\sqrt{\sqrt{x-2}-2}$
Domain: $\{x|\ge6\}$
Work Step by Step
a) $f\circ g = f(g(x)) =$
$(\sqrt{x-2})^2+4=$
$x-2+4=$
$x+2$
Domain: $\{x|x\geq2 \}$
b) $g\circ f = g(f(x)) =$
$\sqrt{x^2+4-2}=$
$\sqrt{x^2+2}$
Domain: $\{x|x\geq2 \}$
c) $f\circ f = f(f(x))=$
$(x^2+4)^2+4=$
$x^4+8x^2+16+4=$
$x^4+8x^2+20$
Domain: $\{x|\Re \}$
d) $g\circ g = g(g(x))=$
$\sqrt{\sqrt{x-2}-2}$
Domain: $\{x|\ge6\}$
