Answer
$f\circ g =\sqrt{3+3x+3x^2}$
Domain: $\{x|\Re\}$
$g\circ f = 1+\sqrt{3x}+x$
Domain: $\{x|x\geq0 \}$
c) $f\circ f = \sqrt[4]{3x}$
Domain: $\{x|x\geq0 \}$
d) $g\circ g =3+3x+4x^2+2x^3+x^4$
Domain: $\{x|\Re\}$
Work Step by Step
$f\circ g = f(g(x)) = $
$\sqrt{3(1+x+x^2)}=$
$\sqrt{3+3x+3x^2}$
Domain: $\{x|\Re\}$
$g\circ f = g(f(x)) =$
$1+\sqrt{3x}+\sqrt{x^2}=$
$1+\sqrt{3x}+x$
Domain: $\{x|x\geq0 \}$
c) $f\circ f = f(f(x))=$
$\sqrt{\sqrt{3x}}=$
$\sqrt[4]{3x}$
Domain: $\{x|x\geq0 \}$
d) $g\circ g = g(g(x))=$
$1+(1+x+x^2)+(1+x+x^2)^2=$
$2+x+x^2+1+x+x^2+x+x^2+x^3+x^2+x^3+x^4=$
$3+3x+4x^2+2x^3+x^4$
Domain: $\{x|\Re\}$