find the composition of f with g and state the domain..
f(x)=(x-3)^(1/2), g(x)=(x^2+3)^(1/2)
tenQ
Okay, you've found the composition so the only thing left to do is state the domain! The only "problem" appears to be square roots. Obviously $\displaystyle x^2+ 3$ is never negative so your only condition is that you must have $\displaystyle (x^2+3)^{1/2}\ge 3$. What values of x satisfy that?
The equation $\displaystyle (x^2+3)^{1/2}= 3$ gives values of x that separate "<" from ">". Find those and determine which of the intervals separated by those values satisfy the inequality.