Answer
$\color{blue}{\bf{(a) -30x-33}\text{; } (-\infty,\infty) } $
$\color{blue}{\bf{(b) -30x+52 }\text{; } (-\infty,\infty) } $
Work Step by Step
We are given the two functions $\bf{f}$ and $\bf{g}$
$\bf{f(x) = -6x+9 }$ and $\bf{g(x) = 5x+7 }$
$\bf(a)$We are asked to find $\bf{ ( f \text{ }\omicron\text{ g} )( x ) }$ and its domain.
${ ( f \text{ }\omicron\text{ g} )( x ) }= -6(5x+7)+9 $
$ -6(5x+7)+9 $
$-30x -42+9$
$\color{blue}{\bf{ -30x-33}}$
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 ) }= 5( -6x+9 )+7 $
$5( -6x+9 )+7 $
$-30x+45+7$
$\color{blue}{\bf{ -30x+52 }}$
The domain is any real number or:
$\color{blue}{\bf{ (-\infty,\infty) }}$
