For `xgt3,f(x)=3x-2` and for `-2lexle2,f(x)=x^(2)-2`, find f(0)+f(4)

Answer

To solve the problem, we need to find the values of \( f(0) \) and \( f(4) \) based on the given piecewise function definitions.

### Step-by-Step Solution:

1. **Identify the function definitions:**
- For \( x > 3 \), \( f(x) = 3x - 2 \)
- For \( -2 \leq x \leq 2 \), \( f(x) = x^2 - 2 \)

2. **Calculate \( f(0) \):**
- Since \( 0 \) lies in the interval \( -2 \leq x \leq 2 \), we will use the second definition of the function.
- Therefore, \( f(0) = 0^2 - 2 = 0 - 2 = -2 \).

3. **Calculate \( f(4) \):**
- Since \( 4 \) is greater than \( 3 \), we will use the first definition of the function.
- Therefore, \( f(4) = 3(4) - 2 = 12 - 2 = 10 \).

4. **Find \( f(0) + f(4) \):**
- Now, we can add the two results together:
- \( f(0) + f(4) = -2 + 10 = 8 \).

### Final Answer:
Thus, \( f(0) + f(4) = 8 \).

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