SOLUTION: For the given functions f and g, find the following and state the domain of each result. f(x)= sqrt x; g(x)=8x-9 (A) (f*g)(x)= (B). (F/g)(x)=

Algebra ->  Functions -> SOLUTION: For the given functions f and g, find the following and state the domain of each result. f(x)= sqrt x; g(x)=8x-9 (A) (f*g)(x)= (B). (F/g)(x)=      Log On


   

Question 937729: For the given functions f and g, find the following and state the domain of each result.
f(x)= sqrt x; g(x)=8x-9
(A) (f*g)(x)=
(B). (F/g)(x)=
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=+sqrt%28+x%29
g%28x%29=8x-9

(A)
%28f%2Ag%29%28x%29=sqrt%28+x%29%2A%288x-9%29
%28f%2Ag%29%28x%29=8x%2Asqrt%28x%29-9sqrt%28x%29
domain:
{ x element R : x%3E=0 } (all non-negative real numbers)

(B).
%28f%2Fg%29%28x%29=sqrt%28+x%29%2F%288x-9%29

the numerator is sqrt%28+x%29 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

%288x-9%29=0=>8x=9%29 =>x=9%2F8

domain is:
{ x element R : 0%3C=x%3C9%2F8 or 8x%3E9 }
(assuming a function from reals to reals)