If f ( x ) = [ x ] , where [ ⋅ ] denotes greatest integral function. Then, check the continuity on ( 1 , 2 ]

Options

A. `20^(2n+1)`
B. an even interger
C. odd interger
D. `40^(2n+1)`

Explanation

To determine the continuity of the function \( f(x) = [x] \), where \([ \cdot ]\) denotes the greatest integer function, on the interval \( (1, 2] \), we can follow these steps:

### Step 1: Understand the Greatest Integer Function
The greatest integer function \([x]\) gives the largest integer less than or equal to \(x\). For example:
- If \(1 < x < 2\), then \([x] = 1\).
- If \(x = 2\), then \([x] = 2\).

### Step 2: Evaluate the Function on the Interval
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