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.

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) (Show Source): You can put this solution on YOUR website!

(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.
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 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!

The domain of g(f(x) might appear to be all Real numbers. However, the f function has a domain of: (so we can avoid negative numbers in the square root) so g(f(x) also has this domain:
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