Answer
$\color{blue}{\bf{(a) 24x+4; }}$$\color{blue}{\bf{ (-\infty,\infty) }}$
$\color{blue}{\bf{(b) 24x+35 ; }}$$\color{blue}{\bf{ (-\infty,\infty) }}$
Work Step by Step
We are given the two functions $\bf{f}$ and $\bf{g}$
$\bf{f(x) = 8x + 12 }$ and $\bf{g(x) = 3x - 1 }$
$\bf(a)$We are asked to find $\bf{ ( f \text{ }\omicron\text{ g} )( x ) }$ and its domain.
${ ( f \text{ }\omicron\text{ g} )( x ) }= 8( 3x - 1) + 12 $
$ 8( 3x - 1) + 12 $
$24x-8+12$
$\color{blue}{\bf{ 24x+4}}$
The domain is any real number or:
$\color{blue}{\bf{ (-\infty,\infty) }}$
$\bf(b)$We are asked to find $\bf{ ( g \text{ }\omicron\text{ f} )( x ) }$ and its domain.
${ ( g \text{ }\omicron\text{ f} )( x ) }= 3(8x + 12 ) - 1 $
$ 3(8x + 12 ) - 1 $
$24x+36-1$
$\color{blue}{\bf{ 24x+35 }}$
The domain is any real number or:
$\color{blue}{\bf{ (-\infty,\infty) }}$