To determine the domain of the function \( y = \frac{x}{\sqrt{x - 6}} \), we need to consider the following:
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The square root is defined only for non-negative numbers. Therefore, we need the expression inside the square root to be greater than zero: \[ x - 6 > 0 \]
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Solving this inequality: \[ x > 6 \]
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The square root being in the denominator means that \( \sqrt{x - 6} \) cannot be zero, which confirms that \( x \) must be strictly greater than 6.
Thus, the function is defined for all \( x \) values greater than 6.
The domain of the function in interval notation is: \[ (6, \infty) \]
Therefore, the correct answer is: A. \( (6, \infty) \).