If `f(x)={{:(3x-1" when "xle0),(x+1" when "xgt0):}`, find f(-1) and f(0).

Answer

To solve the problem, we need to evaluate the piecewise function \( f(x) \) at two specific points: \( f(-1) \) and \( f(0) \).

The function is defined as:
\[ f(x) = \begin{cases} 3x - 1 & \text{when } x \leq 0 \\ x + 1 & \text{when } x > 0 \end{cases} \]

### Step 1: Find \( f(-1) \)

1. Since \(-1\) is less than \(0\), we will use the first part of the piecewise function, which is \( f(x) = 3x - 1 \).
2. Substitute \(-1\) into the function:
\[ f(-1) = 3(-1) - 1 \]
3. Calculate:
\[ f(-1) = -3 - 1 = -4 \]

### Step 2: Find \( f(0) \)

1. Since \(0\) is equal to \(0\), we will again use the first part of the piecewise function, which is \( f(x) = 3x - 1 \).
2. Substitute \(0\) into the function:
\[ f(0) = 3(0) - 1 \]
3. Calculate:
\[ f(0) = 0 - 1 = -1 \]

### Final Answers:
- \( f(-1) = -4 \)
- \( f(0) = -1 \)