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What is the minimum value of [x] ?...

What is the minimum value of [x] ?

A

`-1`

B

0

C

1

D

2

Text Solution

AI Generated Solution

The correct Answer is:
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**.
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Knowledge Check

  • What is the minimum value of |x|?

    A
    `-1`
    B
    0
    C
    2
    D
    4

  • Consider the function f(x) = (x^(2)-1)/(x^(2) + 1) , where x in R What is the minimum value of f(x) ?

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    B
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    `-1`
    D
    2

  • What is the minimum value of f(X)?

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    B
    `1/2`
    C
    `-1`
    D
    2

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