The composition of functions $f \circ g(x)$ means substituting $g(x)$ into $f(x)$. Let's compute $f \circ g(x)$:

1. $f(x) = \sqrt{x + 2}$
2. $g(x) = e^{-x/2}$
3. Substitute $g(x)$ into $f(x)$: $f(g(x)) = f(e^{-x/2}) = \sqrt{e^{-x/2} + 2}.$

Thus, the composition $f \circ g(x)$ is: $f \circ g(x) = \sqrt{e^{-x/2} + 2}.$

Do you want a step-by-step explanation or any further details?

Here are 5 related questions to consider:

1. What is the domain of $f \circ g(x)$?
2. How does $f \circ g(x)$ behave as $x \to \infty$?
3. What is the range of $f \circ g(x)$?
4. Can you compute $f \circ g(0)$?
5. What would $g \circ f(x)$ be in this case?

Tip: For composite functions, ensure the output of the inner function lies in the domain of the outer function.