Find the value of x for which the following expression are defined
(i) `sin^(-1) (3x -2)` (ii) `cos^(-1) (log_(e) x)` (iii) `sec^(-1) (x^(2) -2)`

Explanation

To find the values of \( x \) for which the given expressions are defined, we will analyze each expression one by one.

### (i) \( \sin^{-1}(3x - 2) \)

The function \( \sin^{-1}(y) \) is defined for \( y \) in the interval \([-1, 1]\). Therefore, we need to set up the inequality:

\[
-1 \leq 3x - 2 \leq 1
...