Answer
a. $(f \circ g)(x)=acx+ad+b,$
b. $(g\circ f)(x)=acx+bc+d,$
c. Domain of $f\circ g$ is $x \in \mathbb{R}$ and Domain of $g\circ f(x)$ is $x\in \mathbb{R}$
d. For $f\circ g$ to equal $g \circ f,$ $ad+b$ must be equal to $bc+d$
Work Step by Step
$f(x)=ax+b,$ $g(x)=cx+d$
a. $(f \circ g)(x)=a(cx+d)+b=acx+ad+b,$
b. $(g\circ f)(x)=c(ax+b)+d=acx+bc+d,$
c. Domain of $f\circ g$ is $x \in \mathbb{R}$ and Domain of $g\circ f$ is $x\in \mathbb{R}$
d. $f\circ g=g \circ f,$
$acx+ad+b=acx+bc+d,$
$ad+b=bc+d$. Therefore,
for $f\circ g$ to equal $g \circ f,$ $ad+b$ must be equal to $bc+d$
