https://file.aiquickdraw.com/mathbot/file/1726948225357qztxms1e.jpg

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.

If f(x) = √(1 - x), g(x) = 1 / (2 - x), then (f ∘ g)(x) = ?

Learn how to solve the function composition (f ∘ g)(x) where f(x) = √(1 - x) and g(x) = 1 / (2 - x). This problem involves key concepts such as square roots, rational expressions, and algebraic simplification. Suitable for students in Grades 10-12.

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