Let's break down the problem step by step.

We are given the functions:

• $f(x) = \sqrt{x}$
• $g(x) = x + 6$

We are tasked with finding the following:

a. $(f \circ g)(x)$

This means we need to compute the composition of $f$ and $g$, which is $f(g(x))$.

1. First, substitute $g(x) = x + 6$ into $f(x)$.
2. $f(g(x)) = f(x + 6) = \sqrt{x + 6}$

Thus, $(f \circ g)(x) = \sqrt{x + 6}$.

Let me know if you'd like details for the other parts (b, c, and d), and if you have any questions!

Here are 5 related questions for practice:

1. How do you evaluate $(g \circ f)(x)$?
2. What is the value of $(f \circ g)(3)$?
3. How do you calculate $(g \circ f)(3)$?
4. What is the domain of the function $(f \circ g)(x)$?
5. How do you interpret function composition in real-world applications?

Tip: When composing functions, always substitute the inner function first before applying the outer function.