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The problem asks for the domain of \( f(g(x)) \) where \( f(x) = \sqrt{x} \) and \( g(x) = x - 2 \).

### Step 1: Composition of functions
We are asked to find the domain of \( f(g(x)) \). Since \( f(x) = \sqrt{x} \), for \( f \) to be defined, the argument of the square root must be non-negative:
\[
g(x) = x - 2 \geq 0
\]

### Step 2: Solving the inequality
To ensure \( g(x) = x - 2 \geq 0 \), solve for \( x \):
\[
x - 2 \geq 0 \implies x \geq 2
\]

### Step 3: Conclusion
Thus, the domain of \( f(g(x)) \) is \( x \geq 2 \). The correct answer is:
- **c. \( x \geq 2 \)**.

Do you have any questions, or would you like a further breakdown?

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Here are five related questions for further exploration:

1. What is the domain of \( f(x) = \sqrt{x-3} \)?
2. How do you find the domain of a composition of two functions?
3. If \( g(x) = x^2 - 4 \), what would be the domain of \( f(g(x)) \) if \( f(x) = \sqrt{x} \)?
4. How does the range of \( g(x) \) affect the domain of \( f(g(x)) \)?
5. How would you approach finding the range of \( f(g(x)) \) in this case?

**Tip**: When working with compositions involving square roots, always make sure the expression inside the root is non-negative for the function to be valid.

If f(x) = √x and g(x) = x - 2, what is the correct domain for f(g(x))?

Learn how to determine the domain of the composite function f(g(x)) where f(x) = √x and g(x) = x - 2. This problem involves analyzing the domain restrictions of square root functions and compositions, suitable for students in Grades 9-11.

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