The composition of functions $(f \circ g)(x)$ means applying $g(x)$ first and then applying $f(x)$ to the result. In this case:

1. $g(x) = \sqrt{x^2 + 3}$
2. Now, apply $f(x)$ to the result of $g(x)$:
   $f(g(x)) = f\left(\sqrt{x^2 + 3}\right)$

Since $f(x) = \sqrt{x - 3}$, we substitute $\sqrt{x^2 + 3}$ into $f(x)$:

$(f \circ g)(x) = \sqrt{\left(\sqrt{x^2 + 3}\right) - 3}$

Simplifying the expression inside the square root:

$(f \circ g)(x) = \sqrt{x^2 + 3 - 3} = \sqrt{x^2}$

$(f \circ g)(x) = |x|$

Thus, the composition of $f$ and $g$ is $(f \circ g)(x) = |x|$.

Would you like more details or have any further questions?

Here are 5 related questions:

1. How do you find the domain of a composed function?
2. What is the domain of $f(x) = \sqrt{x-3}$?
3. What is the domain of $g(x) = \sqrt{x^2 + 3}$?
4. How would you compute $(g \circ f)(x)$?
5. How does the absolute value appear in the final result?

Tip: When working with square root functions, always check the domain to ensure you’re not taking the square root of a negative number.