Let [x] denotes the greatest integer less than or equal to x. If `f(x) =[x sin pi x]`, then `f(x)` is

Explanation

To solve the problem where \( f(x) = [x \sin(\pi x)] \), where \([x]\) denotes the greatest integer less than or equal to \(x\), we will analyze the function step by step.

### Step 1: Understanding the Greatest Integer Function
The greatest integer function \([x]\) returns the largest integer less than or equal to \(x\). For example:
- If \(x = 0.5\), then \([0.5] = 0\)
- If \(x = 2.3\), then \([2.3] = 2\)
- If \(x = -1.2\), then \([-1.2] = -2\)

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