Find the domain and range of the function `f(x)="sin"^(-1)(x^(2))/(2)`

Explanation

`f(x)="sin"^(-1)(x^(2))/(2)`
We must have `o le (x^(2))/(2) le 1`
`implies 0le x^(2) le 2`
`implies -sqrt(2) le x le sqrt(2)`
So, domain is `[ -sqrt(2),sqrt(2)]`
Now, ` 0 le (x^(2))/(2) le 1`
`implies sin^(-1) 0 le "sin"^(-1)(x^(2))/(2) le sin^(-1)1`
`implies 0 le "sin"^(-1)(x^(2))/(2) le pi//2`
Hence range is `[0,pi//2]`.