Write the piecewise definition of the function:
`f(x)= [sqrt(x)] ` ,
where [.] denotes the greatest integer function.

Explanation

To write the piecewise definition of the function \( f(x) = [\sqrt{x}] \), where \([.]\) denotes the greatest integer function, we will analyze the function based on the intervals of \(x\).

### Step-by-Step Solution:

1. **Identify the Domain**:
The square root function \(\sqrt{x}\) is defined for \(x \geq 0\). Therefore, the domain of \(f(x)\) is \(x \geq 0\).

2. **Analyze the Intervals**:
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