Let `f(x)=1+|x|, x lt -1`
`[x], x ge -1`, where [.] denotes the greatest integer function.
Then
`f{f(-2,3)}` is equal to

Options

A. 4
B. 2
C. `-3`
D. 3

Answer

To solve the problem, we need to evaluate the function \( f(x) \) given in two parts based on the value of \( x \):

1. \( f(x) = 1 + |x| \) for \( x < -1 \)
2. \( f(x) = [x] \) for \( x \geq -1 \) (where \([x]\) denotes the greatest integer function)

We need to find \( f(f(-2, 3)) \).

### Step 1: Evaluate \( f(-2) \)

Since \(-2 < -1\), we use the first part of the function:

\[ f(-2) = 1 + |-2| = 1 + 2 = 3 \]

### Step 2: Evaluate \( f(3) \)

Since \(3 \geq -1\), we use the second part of the function:

\[ f(3) = [3] = 3 \]

### Step 3: Evaluate \( f(f(-2, 3)) \)

Now we need to evaluate \( f(3) \):

\[ f(3) = 3 \quad \text{(as calculated in Step 2)} \]

### Step 4: Final Evaluation

Now we need to evaluate \( f(3) \) again, which we already found:

\[ f(3) = 3 \]

Thus, the final answer is:

\[ f(f(-2, 3)) = f(3) = 3 \]

### Conclusion

The value of \( f(f(-2, 3)) \) is \( 3 \).