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The function given is \( f(x) = \frac{x}{\sqrt{a}} \), where \( a \) appears to be a constant.

To determine the domain of this function, we need to check for any restrictions on \( x \) based on the nature of the function.

1. **Square Root Constraint**: The square root function is defined as long as the radicand (the expression inside the square root) is non-negative. However, in this case, \( \sqrt{a} \) does not depend on \( x \), and if \( a > 0 \), there is no issue regarding the square root for any real \( x \). If \( a = 0 \), the function would be undefined due to division by zero.

2. **Division by Zero**: The function is undefined if \( a = 0 \), because this would cause division by zero. But as long as \( a > 0 \), there is no issue with division by zero.

Thus, the domain of the function \( f(x) = \frac{x}{\sqrt{a}} \) would be all real numbers as long as \( a > 0 \), meaning \( (-\infty, \infty) \) is the domain of the function.

### Correct Answer: 
The correct choice is **(d) \( (-\infty, \infty) \)**, as highlighted in the image.

Would you like further clarification on this? 

Here are 5 related questions you might find helpful:
1. What would happen to the domain if \( a \) were negative?
2. How would the function change if \( a \) depended on \( x \)?
3. Can the range of this function be determined?
4. What if the function was \( f(x) = \frac{1}{\sqrt{a}} \), how would the domain change?
5. How do you find the domain for more complex functions?

**Tip:** Always check for division by zero and square roots of negative numbers when determining domains!

The domain of the function f(x) = x/√a is

Learn how to find the domain of the function f(x) = x/√a by understanding square root properties and division by zero constraints. Suitable for high school students, this explanation covers key points in determining domains of functions.

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