Find the domain of each of the following real valued functions of real variable: `f(x)=sqrt(x-2)` (ii) `f(x)=1/(sqrt(x^2-1))` (iii) `f(x)=sqrt(9-x^2)` (iv) `f(x)=sqrt((x-2)/(3-x))`

Explanation

To find the domain of the given functions, we need to determine the set of all real numbers \( x \) for which each function is defined. Let's analyze each function step by step.

### (i) \( f(x) = \sqrt{x - 2} \)

1. **Condition for the square root**: The expression inside the square root must be non-negative.
\[ x - 2 \geq 0 \]
...