Find the possible values of `sin^(-1) (1 - x) + cos^(-1) sqrt(x -2)`

1.	Find the possible values of `sin^(-1) (1 - x) + cos^(-1) sqrt(x -2)`
Answer» We have `f(x) = sin^(-1) (1 - x) + cos^(-1) sqrt(x - 2)` We must have `- 1 le (1 - x) le 1` `rArr -2 le - x le 0` `rArr 0 le x le 2 and x -2 ge 0` `rArr 0 le x le 2 and x le 2` `:. X = 2` Thus, expression is defined only for `x = 2` `:. f(2) = sin^(-1) (-1) + cos^(-1) (0)` `= (-pi//2) + (pi//2)` `=0`

Discussion

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