document.write( "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?
\n" ); document.write( "Any help would be greatly appreciated. \n" ); document.write( "

Algebra.Com's Answer #153097 by jsmallt9(3758) $\"\"$ $\"About$

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$\"f%28x%29=sqrt%28x%2B2%29\"$ $\"g%28x%29=x%5E2\"$
\n" ); document.write( "(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.
\n" ); document.write( " $\"f%28x%29=sqrt%28x%2B2%29\"$ 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!
\n" ); document.write( "Similarly $\"g%28x%29+=+x%5E2\"$ is saying that the function g will take whatever you give it and square it, no matter what.

\n" ); document.write( "So when we give the g function the f function, guess what it will try to do? It will square it!
\n" ); document.write( " $\"g%28f%28x%29%29+=+%28f%28x%29%29%5E2+=+%28sqrt%28x+%2B+2%29%29%5E2+=+x+%2B+2\"$
\n" ); document.write( "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: $\"x+%3E=+-2\"$ \n" ); document.write( "

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