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The image you provided appears to contain mathematical notes in Arabic regarding functions and inverses. Let’s go through the key elements:

1. **Definition of the Function**: The function \( f(x) = (\sqrt{x} - \sqrt{a})^2 \) is given. This expression represents the square of the difference between the square root of \( x \) and the square root of a constant \( a \).

2. **Domain of the Function**: It seems the domain \( D_f \) is under discussion. Typically, when dealing with square roots, the argument must be non-negative to keep the function real, so for \( f(x) \), the domain would include values of \( x \) for which \( \sqrt{x} - \sqrt{a} \) is defined, likely implying \( x \geq 0 \).

3. **Limit of the Function**: The notes appear to mention a limit expression:
   \[
   \lim_{x \to a^+} f(x)
   \]
   which likely evaluates the function's behavior as \( x \) approaches \( a \) from the right.

4. **Range of the Function**: There is mention of the range \( I = [0, \sqrt{a}] \), indicating the set of possible values for \( f(x) \), given its domain.

5. **Inverse Function**: There is a note suggesting that \( f \) has an inverse function, likely referring to finding \( f^{-1} \), which maps the range of \( f(x) \) back to its domain.

Would you like a step-by-step solution for finding the inverse of this function or further clarification on any of these topics?

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Here are five questions related to this topic:

1. What steps are involved in finding the domain of a function involving square roots?
2. How can we find the inverse of a quadratic function like \( f(x) = (\sqrt{x} - \sqrt{a})^2 \)?
3. What is the importance of calculating the limit of a function as \( x \) approaches a particular point?
4. How do we determine the range of a function defined on a specific interval?
5. What conditions must a function meet to have an inverse?

**Tip:** When dealing with functions that involve square roots, always consider the constraints on the variable to ensure that the expression remains within the real number set.

Determine the properties of the function f(x) = (√x - √a)^2, including its domain, range, limit as x approaches a, and whether it has an inverse.

Explore the properties of the function f(x) = (√x - √a)^2, including its domain, range, and limits. Learn how to determine if the function has an inverse. Suitable for high school students studying advanced algebra.

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