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

(i) `sin^(-1) (3x -2)` is defined if
`-1 le 3x -2 le 1`
`:. 1 le 3x le 3`
So, `1//3 le x le 1`
(ii) `cos^(-1) (log_(e)x)` is defined if
`-1 le log_(e) x le 1`
`:. e^(-1) le x le e`
(iii) `sec^(-1) (x^(2) -2)` is defined if
`x^(2) - 2 le -1 " or " x^(2) - 2 ge 1`
`:. x^(2) le 1 " or " x^(2) ge 3`
so, `-1 le x le 1 " or " x le -sqrt3 " or ' x ge sqrt3`