The function you provided seems ambiguous due to the lack of parentheses. I'll first interpret it based on common conventions, and then solve accordingly. There are two possible interpretations:

1. **If the square root applies only to \(2x\)** and the denominator is \( \frac{1}{\sqrt{18 - 3x}} \)**:**
   
   \[
   f(x) = \frac{\sqrt{2x} + 1}{\sqrt{18 - 3x}}
   \]

2. **If the square root applies to both \(2x + 1\)**:**
   
   \[
   f(x) = \frac{\sqrt{2x + 1}}{\sqrt{18 - 3x}}
   \]

Please confirm which interpretation is correct, or if another interpretation is intended. Would you like details on solving or analyzing one of these functions?

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### 5 Follow-Up Questions:
1. Would you like to find the domain of the function?
2. Should I explain how to differentiate the function?
3. Would you like a graph of the function for visual understanding?
4. Should I show how to simplify the function further?
5. Are there any particular values of \(x\) you want evaluated?

**Tip:** When dealing with square roots in functions, always ensure that the expression inside the square root is non-negative for real-valued outputs.

Explore the square root function f(x)= √(2x + 1) / √(18 - 3x) with a detailed breakdown of its domain, potential graph, and simplification steps. This problem engages with core algebraic concepts and is suited for high school students in Grades 9-12.

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