Question 1123467

{{{f(x)=x-3}}}; {{{g(x)=9x^2 }}}

a) Find {{{(f+g)(x)}}} What is the domain?

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

{{{(f+g)(x)=x-3+9x^2}}}

{{{(f+g)(x)=9x^2+x-3}}}

domain: {{{R}}} (all real numbers)




b) Find {{{(f-g)(x)}}} What is the domain?

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

{{{(f-g)(x)=x-3-9x^2}}}

{{{(f-g)(x)=-9x^2+x-3}}}

domain: {{{R}}} (all real numbers)



c) Find {{{(f*g)(x)}}} What is the domain?

{{{(f*g)(x)=(x-3)9x^2}}} 

{{{(f*g)(x)=9x^3-27x^2}}} 

domain: {{{R}}} (all real numbers)



d) Find (f/g)(x) What is the domain?

{{{(f/g)(x)=(x-3)/(9x^2)}}}

{{{(f/g)(x)=x/(9x^2)-3/(9x^2)}}}

{{{(f/g)(x)=1/(9 x) - 1/(3 x^2)}}}

domain:{ {{{x}}} element {{{R}}} : {{{x<>0}}} }



e) Find {{{(f+g)(4)}}}

{{{(f+g)(x)=9x^2+x-3}}}....plug in {{{4}}} for {{{x}}}

{{{(f+g)(4)=9*4^2+4-3}}}

{{{(f+g)(4)=145}}}



f) Find {{{(f-g)(3)}}}

{{{(f-g)(x)=-9x^2+x-3}}}...plug in {{{3}}} for {{{x}}}

{{{(f-g)(3)=-9*3^2+3-3}}}

{{{(f-g)(3)=-81}}}



g) Find {{{(f*g)(2)}}}

{{{(f*g)(x)=9x^3-27x^2}}} ....plug in {{{2}}} for {{{x}}}

{{{(f*g)(2)=9*2^3-27*2^2}}}

{{{(f*g)(2)=-36}}}



h) Find {{{(f/g)(2)}}}

{{{(f/g)(x)=1/(9 x) - 1/(3 x^2)}}}....plug in {{{2}}} for {{{x}}}

{{{(f/g)(2)=1/(9 *2) - 1/(3 *2^2)}}}


{{{(f/g)(2)=1/18 - 1/12}}}

{{{(f/g)(2)=-1/36}}}