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

Options

A. 0
B. `{-1,1}
C. 2
D. -1/2

Answer

A

Explanation

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`