Let `f(x) = 1 + |x|,x < -1 [x], x >= -1, where [*]` denotes the greatest integer function.Then `f { f (- 2.3)}` is equal to

Explanation

To solve the problem, we need to evaluate the function \( f(x) \) defined as follows:

\[ f(x) = \begin{cases} 1 + |x| & \text{if } x < -1 \\ [x] & \text{if } x \geq -1 \end{cases} \]

We need to find \( f(f(-2.3)) \).

### Step 1: Calculate \( f(-2.3) \)

Since \(-2.3 < -1\), we use the first case of the function:

\[ f(-2.3) = 1 + |-2.3| \]

Calculating the absolute value:

\[ |-2.3| = 2.3 \]

Now substituting back into the function:

\[ f(-2.3) = 1 + 2.3 = 3.3 \]

### Step 2: Calculate \( f(f(-2.3)) = f(3.3) \)

Now we need to evaluate \( f(3.3) \). Since \( 3.3 \geq -1\), we use the second case of the function:

\[ f(3.3) = [3.3] \]

The greatest integer function \( [3.3] \) gives us the largest integer less than or equal to \( 3.3 \):

\[ [3.3] = 3 \]

### Final Result

Thus, we have:

\[ f(f(-2.3)) = f(3.3) = 3 \]

The final answer is:

\[ \boxed{3} \]