SOLUTION: Over the set of real numbers what is the domain of the composite function g(f(x)) F(x)=3 - x, G(y)=square root y G(F(X))=SQUARE ROOT 3-X X>3 X greater than equal to 3 X le

Algebra ->  Functions -> SOLUTION: Over the set of real numbers what is the domain of the composite function g(f(x)) F(x)=3 - x, G(y)=square root y G(F(X))=SQUARE ROOT 3-X X>3 X greater than equal to 3 X le      Log On


   

Question 930633: Over the set of real numbers what is the domain of the composite function g(f(x))
F(x)=3 - x, G(y)=square root y
G(F(X))=SQUARE ROOT 3-X
X>3
X greater than equal to 3
X less then equal to 3
All real numbers
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
For any real number x, you can get an F%28x%29 .
In other words, the domain of F%28x%29 is all the real numbers, with no restriction.
G%28F%28x%29%29=sqrt%283-x%29 only exists when 3-x%3E0<--->3%3E=x ,
so the domain of G%28F%28x%29%29 is
all real numbers x such that x%3C=3 (x is less than or equal to 3).