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**Analyzing the content...**The image contains a problem regarding functions and their behavior.

### Problem:
It is given that \(f(x) = \sqrt{3 - x}\) and \(g(x) = \frac{2}{x + 1}\). We need to find the domain of the composition function \( (f \circ g)(x) = f(g(x)) \).

### Step-by-step Solution:

1. **Domain of \(f(x) = \sqrt{3 - x}\):**

   For the square root function to be defined, the expression inside the square root must be non-negative:

   \[
   3 - x \geq 0
   \]

   Solving for \(x\):

   \[
   x \leq 3
   \]

   Thus, the domain of \(f(x)\) is \( (-\infty, 3] \).

2. **Domain of \(g(x) = \frac{2}{x + 1}\):**

   For the fraction to be defined, the denominator must not be zero:

   \[
   x + 1 \neq 0 \implies x \neq -1
   \]

   Thus, the domain of \(g(x)\) is \( (-\infty, -1) \cup (-1, \infty) \).

3. **Domain of the composition function \( (f \circ g)(x) = f(g(x)) \):**

   To find the domain of the composition, we need to determine the set of all \(x\) values that are in the domain of \(g(x)\) such that \(g(x)\) is in the domain of \(f(x)\). 

   Since \(f(x) = \sqrt{3 - x}\), we need:

   \[
   3 - g(x) \geq 0.
   \]

   Substituting \(g(x) = \frac{2}{x + 1}\):

   \[
   3 - \frac{2}{x + 1} \geq 0.
   \]

   Rearranging this inequality:

   \[
   3(x + 1) - 2 \geq 0,
   \]

   \[
   3x + 3 - 2 \geq 0,
   \]

   \[
   3x + 1 \geq 0,
   \]

   \[
   x \geq -\frac{1}{3}.
   \]

4. **Combine the domain conditions:**

   We also know that \(x \neq -1\). Combining the conditions \(x \geq -\frac{1}{3}\) and \(x \neq -1\), we get the domain:

   \[
   x \in \left[-\frac{1}{3}, \infty\right) \setminus \{-1\}.
   \]

### Conclusion:
The domain of the function \( (f \circ g)(x) \) is:

\[
\left[-\frac{1}{3}, \infty\right) \setminus \{-1\}.
\]

Would you like more details on any specific step or do you have any questions?

### Follow-up Questions:
1. What is the range of the composition function \( (f \circ g)(x) \)?
2. How would you find the domain of \( (g \circ f)(x) \) instead?
3. Can you explain why the composition of two functions depends on the range of the inner function?
4. What happens to the domain if both functions \(f(x)\) and \(g(x)\) are modified?
5. How would you graph the composition function \( (f \circ g)(x) \)?

### Tip:
Always carefully consider the domains of

Find the domain of the composition function (f ∘ g)(x) = f(g(x)) where f(x) = √(3 - x) and g(x) = 2/(x + 1).

Learn how to find the domain of the composition function (f ∘ g)(x) = f(g(x)) where f(x) = √(3 - x) and g(x) = 2/(x + 1). This solution explores concepts like domain restrictions for square root and rational functions, suitable for high school math students (Grades 10-12).

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