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Find [2.75], if [x] denotes greatest int...

Find `[2.75], if [x]` denotes greatest integer not greater than x ?

A

2

B

3

C

`0.75`

D

`1.75`

Text Solution

AI Generated Solution

The correct Answer is:
To find the greatest integer less than or equal to 2.75, denoted as \([2.75]\), we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Definition**: The greatest integer function, denoted as \([x]\), gives the largest integer that is less than or equal to \(x\). 2. **Identify the Range**: For \(x = 2.75\), we need to find the integer values that are less than or equal to 2.75. The integers around 2.75 are 2 and 3. 3. **Determine the Greatest Integer**: - The integer 2 is less than 2.75. - The integer 3 is greater than 2.75. - Therefore, the greatest integer that is not greater than 2.75 is 2. 4. **Conclusion**: Thus, we can conclude that \([2.75] = 2\). ### Final Answer: \[ [2.75] = 2 \]
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