What is the minimum value of [x] ?

Options

A. `-1`
B. 0
C. 1
D. 2

Answer

To find the minimum value of the greatest integer function, denoted as [x], we need to understand how this function operates.

### Step-by-Step Solution:

1. **Understanding the Greatest Integer Function**: The greatest integer function, denoted as [x], returns the largest integer that is less than or equal to x. For example:
- [1.47] = 1 (since 1 is the largest integer ≤ 1.47)
- [4] = 4 (since 4 is already an integer)
- [9.99] = 9 (since 9 is the largest integer ≤ 9.99)
- [-0.99] = -1 (since -1 is the largest integer ≤ -0.99)

2. **Identifying Possible Values**: The function can take any real number as input, which means x can be any real number, including negative numbers.

3. **Finding the Minimum Value**:
- The minimum value of [x] occurs when x is just below 0. For example, if x is -0.1, then [x] = -1.
- As x approaches 0 from the left (negative side), the greatest integer function will yield -1.
- If x is exactly 0, then [0] = 0, which is greater than -1.

4. **Conclusion**: Therefore, the minimum value of the greatest integer function [x] is -1.

### Final Answer:
The minimum value of [x] is **-1**.