Answer
$f\circ g(x)=8x+1$; domain: all reals, $(-\infty,\infty)$
$g\circ f(x)=8x+11$; domain: all reals, $(-\infty,\infty)$
$f\circ f(x=4x+9$; domain: all reals, $(-\infty,\infty)$
$g\circ g(x)=16x-5$; domain: all reals, $(-\infty,\infty)$
Work Step by Step
f(x) is defined for all x,
g(x) is defined for all x
$f\circ g(x)=f[g(x)]=2g(x)+3$
$=2(4x-1)+3=8x-2+3=8x+1$,
domain: all reals, $(-\infty,\infty)$
$g\circ f(x)=g[f(x)]=4f(x)-1$
$=4(2x+3)-1=8x+12-1=8x+11$
domain: all reals, $(-\infty,\infty)$
$f\circ f(x)=f[f(x)]=2f(x)+2$
$=2(2x+3)+3=4x+6+3=4x+9$
domain: all reals, $(-\infty,\infty)$
$g\circ g(x)=g[g(x)]=4g(x)-1$
$=4(4x-1)-1=16x-4-1=16x-5$
domain: all reals, $(-\infty,\infty)$
