Answer
a) $f\circ g = 4x^4+12x^2+10$
Domain: $\{x| \Re\}$
b) $g\circ g =2x^4+4x^2+5$
Domain: $\{x|\Re\}$
c) $f\circ f =x^4+2x^2+2$
Domain: $\{x|\Re\}$
d) $g\circ g = 8x^4+24x^2+21$
Domain: $\{x|\Re\}$
Work Step by Step
a) $f\circ g = f(g(x)) = $
$(2x^2+3)^2+1=$
$4x^4+12x^2+9+1=$
$4x^4+12x^2+10$
Domain: $\{x| \Re\}$
b) $g\circ g = g(g(x)) =$
$2(x^2+1)^2+3=$
$2(x^4+2x^2+1)+3=$
$2x^4+4x^2+2+3=$
$2x^4+4x^2+5$
Domain: $\{x|\Re\}$
c) $f\circ f = f(f(x))=$
$(x^2+1)^2+1=$
$x^4+2x^2+1+1=$
$x^4+2x^2+2$
Domain: $\{x|\Re\}$
d) $g\circ g = g(g(x))=$
$2(2x^2+3)^2+3=$
$2(4x^4+12x^2+9)+3=$
$8x^4+24x^2+18+3=$
$8x^4+24x^2+21$
Domain: $\{x|\Re\}$
