Question 1048528

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

find {{{f/g}}} 

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

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


and the domain is:

if {{{(x-3)=0}}}->{{{highlight(x=3)}}}; so,{{{highlight(x<3)}}} or {{{highlight(x>3)}}}
to have a solution for {{{sqrt(2x-1)}}}, {{{(2x-1)}}} cannot be equal to zero

if {{{(2x-1)=0}}}->{{{2x=1}}}->{{{highlight(x=1/2)}}};so, {{{highlight(x>1/2)}}}
 
so, exclude {{{x=3}}} and {{{highlight(x=1/2)}}} and domain is
 
{ {{{x}}} element {{{R}}} : {{{1/2<=x<3}}} or {{{x>3}}} }


{{{ graph( 600, 600, -10, 10, -10, 10, (x-3)sqrt(2x-1)) }}}