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The piecewise function \( f(x) \) is defined as:

\[
f(x) = 
\begin{cases} 
x - 2, & x < 3 \\ 
x + 3, & x \geq 3 
\end{cases}
\]

We are asked to find \( f(2) \).

To determine \( f(2) \), we need to check which part of the piecewise function applies when \( x = 2 \).

Since \( 2 < 3 \), we use the first part of the function, \( f(x) = x - 2 \).

Substitute \( x = 2 \) into this part:

\[
f(2) = 2 - 2 = 0
\]

### Answer:
\[
f(2) = 0
\]

Would you like a detailed explanation on piecewise functions or have any questions?

### Related Questions:
1. How do we evaluate a piecewise function for a given input?
2. What is the general method to determine which part of a piecewise function to use?
3. Can a piecewise function be continuous at the point where it switches?
4. How would we find \( f(3) \) for this function?
5. What are the applications of piecewise functions in real-world scenarios?

### Tip:
Always check the condition on \( x \) to select the correct expression in a piecewise function before substituting values.

إذا كانت \( f(x) = \begin{cases} x - 2, & x < 3 \\ x + 3, & x \geq 3 \end{cases} \) فإن \( f(2) \) تساوي

Learn how to evaluate the piecewise function f(x) = {x - 2 if x < 3, x + 3 if x >= 3} at x = 2. This problem explains the process of selecting the appropriate function expression based on conditions. Suitable for students in Grades 6-8.

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