Answer
$f\circ g(x)=|2x+3|;\qquad $ domain: $(-\infty,\infty)$
$ g\circ f(x)=2|x|+3 ; \quad$ domain: $(-\infty,\infty)$
$ f\circ f(x)=|x|; \quad$ domain: $(-\infty,\infty)$
$ g\circ g(x)=4x+9; \quad$ domain: $(-\infty,\infty)$
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)]= |g(x)|\quad$on the domain of $g$(x)
$=|2x+3|\quad$ on $(-\infty,\infty)$
$=|2x+3|;\qquad $ domain: $(-\infty,\infty)$
$g\circ f(x)=g[f(x)]=2f(x)+3 \quad$on the domain of f(x),\
$=2|x|+3 ; \quad$ domain: $(-\infty,\infty)$
$ f\circ f(x)=f[f(x)]=|f(x)|,\qquad$on the domain of f(x)
$=||x||,\quad $ on $(-\infty,\infty)$
$=|x|; \quad$ domain: $(-\infty,\infty)$
$ g\circ g(x)=g[g(x)]=2g(x)+3 \quad$on the domain of $g$(x)
$=2(2x+3)+3\quad$on $(-\infty,\infty)$
$=4x+9; \quad$ domain: $(-\infty,\infty)$
