SOLUTION: f(x)=sq.root of x+2 ang g(x)=x^2 A) Find (gOf)(x) b) What is the domain of the composition function? Any help would be greatly appreciated.

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Question 194539: f(x)=sq.root of x+2 ang g(x)=x^2 A) Find (gOf)(x) b) What is the domain of the composition function?
Any help would be greatly appreciated.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=sqrt%28x%2B2%29 g%28x%29=x%5E2
(gOf)(x) means "g of f(x)" or g(f(x)). To figure this out it helps if you understand what the function equations are telling you.
f%28x%29=sqrt%28x%2B2%29 is saying that the function f will take whatever you give it add 2 to it and then find the square root. It will add 2 and find a square root no matter what you give it!
Similarly g%28x%29+=+x%5E2 is saying that the function g will take whatever you give it and square it, no matter what.

So when we give the g function the f function, guess what it will try to do? It will square it!
g%28f%28x%29%29+=+%28f%28x%29%29%5E2+=+%28sqrt%28x+%2B+2%29%29%5E2+=+x+%2B+2
The domain of g(f(x) might appear to be all Real numbers. However, the f function has a domain of: x+%3E=+-2 (so we can avoid negative numbers in the square root) so g(f(x) also has this domain: x+%3E=+-2