Composition of Functions

Question

Express the function y=sqrt(x^2+9) as a composition y=f(g(x)) of two simpler functions y=f(u) and u=g(x).

I am not sure how to divide a problem like this into a g function. I understand that if I can find the value of g then that can walk me through the rest of the problem, but I need help with the first step.

Answer 1

Think of f() as the overall structural function sqrt(of something)

And then THAT something is g() = x^2+9

So f=sqrt(x)

and

g=x^2+9

Answer 2

Express the function y=sqrt(x^2+9) as a composition y=f(g(x)) of two simpler functions y=f(u) and u=g(x).

Easy. g(x) is the innermost or the embedded function:

make g(x) = x²+9

then f(x) = √x

then h(x) = f(g(x))