Answer
$\color{blue}{\bf{ 5x^2 - x + 2 }; \text{ domain } (-\infty,\infty) }$
$\color{blue}{\bf{ 3x^2+ 5x-2 }; \text{ domain } (-\infty,\infty) }$
$\color{blue}{\bf{ 4x^4-10x^3+2x^2+4x }; \text{ domain } (-\infty,\infty) }$
$\color{blue}{\bf{ \dfrac{ 4x^2 + 2x }{ x^2 - 3x + 2 } }; \text{ domain } (-\infty,\infty) }$
Work Step by Step
We are given the two functions $\bf{f}$ and $\bf{g}$
$\bf{f(x) = 4x^2 + 2x }$ and $\bf{g(x) = x^2 - 3x + 2 }$
We are asked to find $\bf{( f+g )( x )}$ and its domain:
$( 4x^2 + 2x )+( x^2 - 3x + 2 ) $
$4x^2 + x^2+ 2x - 3x + 2 $
$\color{blue}{\bf{ 5x^2 - x + 2 }}$
$x$ can be any real number so its domain is:
$\color{blue}{\bf{ (-\infty,\infty) }}$
We are asked to find $\bf{( f-g )( x )}$ and its domain:
$( 4x^2 + 2x )-( x^2 - 3x + 2 )$
$ 4x^2- x^2+ 2x +3x-2 $
$\color{blue}{\bf{ 3x^2+ 5x-2 }}$
$x$ can be any real number so its domain is:
$\color{blue}{\bf{ (-\infty,\infty) }}$
We are asked to find $\bf{( fg )( x )}$ and its domain:
$( 4x^2 + 2x )( x^2 - 3x + 2 ) $
$4x^4-12x^3+8x^2+2x^3-6x^2+4x$
$\color{blue}{\bf{ 4x^4-10x^3+2x^2+4x }}$
$x$ can be any real number so its domain is:
$\color{blue}{\bf{ (-\infty,\infty) }}$
We are asked to find $\bf{( \dfrac{f }{ g} )( x)}$ and its domain:
$\color{blue}{\bf{ \dfrac{ 4x^2 + 2x }{ x^2 - 3x + 2 } }}$
$x$ can be any real number so its domain is:
$\color{blue}{\bf{ (-\infty,\infty) }}$
