SOLUTION: Let f(x)= √(x-3) ,g(x)= x^2+8 Find the domains of g(f (x))

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Question 1005167: Let f(x)= √(x-3) ,g(x)= x^2+8
Find the domains of g(f (x))
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

if f%28x%29=+sqrt%28x-3%29 ,g%28x%29=++x%5E2%2B8
then first we apply f, then apply g to that result:
g%28f+%28x%29%29=g%28sqrt%28x-3%29%29
g%28sqrt%28x-3%29%29=+%28sqrt%28x-3%29%29%5E2%2B8
g%28sqrt%28x-3%29%29=+x-3%2B8
g%28sqrt%28x-3%29%29=+x%2B5
the domain is:R (all real numbers)