You want to find the inverse of the function \( f(x) = \sqrt{2x + 3} \). Here's the step-by-step process to solve for \( f^{-1}(x) \):

### Step 1: Replace \( f(x) \) with \( y \)
\[
y = \sqrt{2x + 3}
\]

### Step 2: Swap \( x \) and \( y \) to start solving for the inverse
\[
x = \sqrt{2y + 3}
\]

### Step 3: Square both sides to remove the square root
\[
x^2 = 2y + 3
\]

### Step 4: Solve for \( y \)
\[
x^2 - 3 = 2y
\]
\[
y = \frac{x^2 - 3}{2}
\]

Thus, the inverse function is:
\[
f^{-1}(x) = \frac{x^2 - 3}{2}
\]

### Final Answer:
\[
f^{-1}(x) = \frac{x^2 - 3}{2}
\]

Would you like any further details or explanations on this? 

Here are 5 questions related to this process:
1. What are the steps to verify if the inverse function is correct?
2. How do domain restrictions affect the inverse of a function like this?
3. What is the domain of the original function, \( f(x) = \sqrt{2x + 3} \)?
4. How would the graph of the inverse function compare to the original function?
5. Can you find the inverse of other types of radical functions?

**Tip:** Always check that the domain and range of a function and its inverse align correctly!

Learn how to find the inverse of the function f(x) = √2x + 3 through a step-by-step process. This problem covers key concepts in algebra and inverse functions, including solving for y and removing square roots. Suitable for students in Grades 10-12.

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