Question 937729


{{{f(x)= sqrt( x)}}} 
{{{g(x)=8x-9}}}


(A) 

{{{(f*g)(x)=sqrt( x)*(8x-9)}}}

{{{(f*g)(x)=8x*sqrt(x)-9sqrt(x)}}}

domain:

{ {{{x}}} element {{{R}}} : {{{x>=0}}} }  (all non-negative real numbers)


(B). 

{{{(f/g)(x)=sqrt( x)/(8x-9)}}}


the numerator is {{{sqrt( x)}}} which means {{{x}}} can be {{{0}}} or any positive number because if {{{x}}} is negative number we will have complex solution

denominator cannot be equal to zero; so, find values that make it equal to zero and exclude them from set of solutions


{{{(8x-9)=0}}}=>{{{8x=9)}}} =>{{{x=9/8}}}


domain is:

{ {{{x}}} element {{{R}}} : {{{0<=x<9/8}}} or {{{8x>9}}} }
(assuming a function from reals to reals)