The domain of the function `f(x) = sqrt(x-sqrt(1-x^(2)))` is

Options

A. `[1,-1//sqrt2)] cup [1//sqrt(2),1]`
B. [-1,1]
C. `(-oo,-1//2) cup [1//sqrt(2),oo)`
D. `[1//sqrt(2),1]`

Answer

D

Explanation

We observe that f(x) is defined or f(x) assumes rela value , if
`implies x-sqrt(1-x^(2)) ge 0 and 1-x^(2) gt0`
`implies x ge sqrt(1-x^(2)) and 0 le x le 1 " " [ :' x ge sqrt(1-x^(2)) implies x ge 0]`
`implies x^(2) ge 1-x^(2) and 0 le x le 1 `
`implies 2x^(2)-1 ge 0 and 0 le x le 1 `
`implies x in (-oo, -1//sqrt(2),oo) and 0 le x le 1 `
`implies x in [1//sqrt(2) , 1]`