If `f(x)={(x-2,,xlt2),(3,,x=2),(x+2,,xgt3):}`,then find f(8).

Answer

To find the value of \( f(8) \) for the given piecewise function \( f(x) \), we will follow these steps:

1. **Identify the piecewise function**: The function is defined as follows:
- \( f(x) = x - 2 \) for \( x < 2 \)
- \( f(x) = 3 \) for \( x = 2 \)
- \( f(x) = x + 2 \) for \( x > 3 \)

2. **Determine which interval \( x = 8 \) falls into**:
- We need to check the conditions for each piece of the function.
- Since \( 8 > 3 \), we see that \( 8 \) falls into the third interval where \( x > 3 \).

3. **Use the appropriate function definition**:
- Since \( 8 \) is in the interval \( x > 3 \), we use the definition \( f(x) = x + 2 \).

4. **Substitute \( x = 8 \) into the function**:
- Now we calculate \( f(8) \):
\[ f(8) = 8 + 2 \]

5. **Calculate the result**:
- Performing the addition gives us:
\[ f(8) = 10 \]

Thus, the final answer is:
\[ f(8) = 10 \]