Question 1134031


Let {{{f (x) = 3x^2 + 4x - 8 }}}and{{{ g(x) = 3 - 2x}}}. 
a.	Evaluate the function 

{{{(g - f)(x)}}} for{{{ x = - 4}}}. .....first find {{{(g - f)(x)}}}

{{{(g - f)(x)=3 - 2x-( 3x^2 + 4x - 8)}}}

{{{(g - f)(x)=3 - 2x- 3x^2 - 4x + 8}}}

{{{(g - f)(x)= - 3x^2 - 6x + 11}}}

no find find {{{(g - f)( - 4)}}}:

{{{(g - f)(-4)= - 3(-4)^2 - 6(-4) + 11}}}
{{{(g - f)(-4)= - 3(16) + 24 + 11}}}
{{{(g - f)(-4)= - 48 + 35}}}
{{{(g - f)(-4)= -13}}}


b.	Evaluate the function {{{(fg)(x)}}} for {{{x = - 4}}}: 
{{{(g *f)(x)=(3 - 2x)( 3x^2 + 4x - 8)}}}
{{{(g *f)(x)= 9x^2 + 12x - 24-6x^3-8x^2+16x}}}
{{{(g *f)(x)=-6x^3+ x^2 + 28x - 24}}}

now find {{{(f *g)( - 4)}}}: 

{{{(g *f)(-4)=-6(-4)^3+ (-4)^2 + 28(-4) - 24}}}

{{{(g *f)(-4)=-6(-64)+ 16 -112 - 24}}}

{{{(g *f)(-4)=384+ 16 -112 - 24}}}

{{{(g *f)(-4)=264}}}


c.	Show the difference function {{{(f - g)(x)}}}. Simplify the function as much as possible. Show work. 

{{{(g - f)(x)=g(x)-f(x)}}}

{{{(g - f)(x)=(3 - 2x)-( 3x^2 + 4x - 8)}}}

{{{(g - f)(x)=3 - 2x- 3x^2 - 4x + 8}}}

{{{(g - f)(x)= - 3x^2 - 6x + 11}}}