Answer
$\color{blue}{\bf{ (a) (x^2 + 3x - 1)^3 ; (-\infty,\infty) }}$
$\color{blue}{\bf{ (b) x^6 + 3x^3 - 1 ; (-\infty,\infty) }}$
Work Step by Step
We are given the two functions $\bf{f}$ and $\bf{g}$
$\bf{f(x) = x^3 }$ and $\bf{g(x) = x^2 + 3x - 1 }$
$\bf(a)$We are asked to find $\bf{ ( f \text{ }\omicron\text{ g} )( x ) }$ and its domain.
${ ( f \text{ }\omicron\text{ g} )( x ) }= (x^2 + 3x - 1)^3 $
$\color{blue}{\bf{ (x^2 + 3x - 1)^3 }}$
$x$ can be 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 ) }= (x^3)^2 + 3(x^3) - 1 $
$\color{blue}{\bf{ x^6 + 3x^3 - 1 }}$
$x$ can be any real number or:
$\color{blue}{\bf{ (-\infty,\infty) }}$
