expressing function as a composition

Question

Express function y=sqrt(x² + 3) as a composition y=f(g(x)) of two simpler functions y=f(u) and u=g(x)

Answer 1

We can split this into a composite function by letting the square root be one function and whatever is inside the square root be the other function. So:

 

f(x) = sqrt(x)

g(x) = x² + 3

 

Therefore, f(g(x)) = sqrt(x² + 3)