SOLUTION: Over the set of real numbers, what is the domain of the composite function G(F(x))? F(x) = 3 - x, G(y) = √y G(F(x)) = √3-x possible awnsers are: A. x > 3

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) = √y G(F(x)) = √3-x possible awnsers are: A. x > 3      Log On


   

Question 144971: Over the set of real numbers, what is the domain of the composite function G(F(x))?
F(x) = 3 - x, G(y) = √y
G(F(x)) = √3-x
possible awnsers are:
A. x > 3
B. x 3
C. x 3
D. All real numbers


Answer by solver91311(24713) About Me  (Show Source):
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The domain of F is all reals because there are no real values of x that would make F undefined. G, on the other hand, requires that y%3E=0. Saying G(F(x)) is the same as saying y=F%28x%29=3-x, so the question becomes 'What values of x make y less than 0?'

3-x%3C0
-x%3C-3
x%3E3

So anytime x%3E3, y%3C0 and G would be undefined. Therefore the domain of G(F(x)) is x%3C=3. In interval notation: (infinity,3]