Question 752930


For {{{f(x)=x^2-3x-4}}}, and {{{g(x)=x-4}}}
Evaluate and simplify the following:

a) for what {{{x}}}, is {{{f(x)=g(x)}}}?

{{{x^2-3x-4=x-4}}}....solve for {{{x}}}

{{{x^2-3x+x-4+4=0}}}

{{{x^2-2x=0}}}...factor

{{{x(x-2)=0}}}...use zero product rule

solutions:

{{{highlight(x=0)}}}

if {{{x-2=0}}} => {{{highlight(x=2)}}}



b) 

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

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

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

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


c) 

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

{{{(f/g)(x)=(x^2-3x-4)/(x-4)}}}...write {{{-3x }}} as {{{x-4x}}}


{{{(f/g)(x)=(x^2+x-4x-4)/(x-4)}}}..group


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


{{{(f/g)(x)=(x(x+1)-4(x+1))/(x-4)}}}


{{{(f/g)(x)=((x-4)(x+1))/(x-4)}}}


{{{(f/g)(x)=(cross((x-4))(x+1))/cross((x-4))}}}


{{{(f/g)(x)=x+1}}}