Find the domain and range of the following:
(a). f(x) = 1/√(x − 3)

Let's analyze the function \( f(x) = \frac{1}{\sqrt{x - 3}} \) to determine its domain and range.

### Domain:
The domain of a function consists of all possible input values (x-values) for which the function is defined.

1. **Square Root Condition**: The square root function, \( \sqrt{x - 3} \), is only defined when \( x - 3 \geq 0 \). Therefore, \( x \geq 3 \).

2. **Denominator Condition**: The function also has a denominator, so \( \sqrt{x - 3} \) cannot be zero. This occurs when \( x - 3 \neq 0 \), i.e., \( x \neq 3 \).

Combining these two conditions, we get \( x > 3 \). Therefore, the **domain** of \( f(x) \) is:

\[
\text{Domain} = (3, \infty)
\]

### Range:
The range of a function is the set of all possible output values (y-values) that the function can take.



Learn how to find the domain and range of the function f(x) = 1/√(x − 3) with a detailed analysis. This problem covers the square root function and its domain restrictions, suitable for advanced high school students.

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