Question 194539
{{{f(x)=sqrt(x+2)}}} {{{g(x)=x^2}}}
(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(x)=sqrt(x+2)}}} is saying that the function f will take <b>whatever you give it</b> 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(x) = x^2}}} is saying that the function g will take whatever you give it and square it, no matter what.<br>
So when we give the g function the f function, guess what it will try to do? It will square it!
{{{g(f(x)) = (f(x))^2 = (sqrt(x + 2))^2 = x + 2}}}
The domain of g(f(x) might appear to be all Real numbers. However, the f function has a domain of: {{{x >= -2}}} (so we can avoid negative numbers in the square root) so g(f(x) also has this domain: {{{x >= -2}}}