Let's solve the problem.

The functions given are:

$f(x) = \sqrt{1 - x}, \quad g(x) = \frac{1}{2 - x}$

We are asked to find $(f \circ g)(x)$, which is the composition of functions. This means we need to substitute $g(x)$ into $f(x)$.

1. Start by finding $f(g(x))$: $f(g(x)) = f\left(\frac{1}{2 - x}\right) = \sqrt{1 - \frac{1}{2 - x}}$

2. Simplify the expression inside the square root: $1 - \frac{1}{2 - x} = \frac{(2 - x) - 1}{2 - x} = \frac{1 - x}{2 - x}$

   Therefore: $f(g(x)) = \sqrt{\frac{1 - x}{2 - x}}$

Now, looking at the options, the correct answer is the first one, which shows:

$\boxed{\sqrt{\frac{1 - x}{2 - x}}}$

So the circled answer is correct.

Do you want further details or have any questions?

Here are some related questions:

1. How do you compose two functions algebraically?
2. Can you find $f(g(x))$ for different $f(x)$ and $g(x)$?
3. What are the conditions under which compositions of functions are defined?
4. How would the solution change if $f(x)$ and $g(x)$ were different?
5. What other operations can be performed with functions aside from composition?

Tip: When dealing with function composition, always carefully substitute the entire inner function into the outer function.