Answer
$\color{blue}{\bf{ (a) x^4+x^2-2 ; (-\infty,\infty) }}$
$\color{blue}{\bf{ (b) (x+2)^4+(x+2)^2-4 ; (-\infty,\infty) }}$
Work Step by Step
We are given the two functions $\bf{f}$ and $\bf{g}$
$\bf{f(x) = x + 2 }$ and $\bf{g(x) = x^4+x^2-4 }$
$\bf(a)$We are asked to find $\bf{ ( f \text{ }\omicron\text{ g} )( x ) }$ and its domain.
${ ( f \text{ }\omicron\text{ g} )( x ) }= x^4+x^2-4+2 $
$\color{blue}{\bf{ x^4+x^2-2 }}$
$x$ 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+2)^4+(x+2)^2-4 $
$\color{blue}{\bf{ (x+2)^4+(x+2)^2-4 }}$
$x$ can be any real number or:
$\color{blue}{\bf{ (-\infty,\infty) }}$
