What is the range of `f(x)=[([x])/(x)].`

Explanation

To find the range of the function \( f(x) = \frac{[x]}{x} \), where \([x]\) denotes the greatest integer less than or equal to \( x \), we can analyze the behavior of this function for both positive and negative values of \( x \).

### Step 1: Analyze the function for positive values of \( x \)

1. Let \( x \) be a positive real number. Then \([x]\) is the greatest integer less than or equal to \( x \).
2. For any \( x \) in the interval \( [n, n+1) \) where \( n \) is a positive integer, we have \([x] = n\).
3. Thus, the function can be expressed as:
\[
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