Question 1190030
{{{f(x) = 2x-3}}}

{{{g(x)=sqrt(3x-1)}}}

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


{{{(f*g)=(2x-3)(sqrt(3x-1))}}}

{{{(f*g)=2x*sqrt(3x -1) - 3sqrt(3 x-1)}}}

Domain: all except the value of {{{x}}} that makes {{{(3 x - 1)}}} negative, so

{{{3x - 1}}} must be equal or greater than zero

{{{3x - 1>=0}}}

{{{3x >=1}}}

{{{x >=1/3}}}

domain is

{ {{{x}}} element {{{R}}} : {{{x>=1/3}}} }


interval notation: [{{{1/3}}},{{{infinity}}})



 and 


{{{f-g=2x-3-sqrt(3x-1)}}}


domain is

{ {{{x}}} element {{{R}}} : {{{x>=1/3}}} }


interval notation: [{{{1/3}}},{{{infinity}}})