Find the domain for `f(x)=sin^(-1)((1+x^2)/(2x))`

Explanation

`f(x) = sin^-1((1+x^2)/(2x))`

We know `sin theta` lies between `-1` and `1`.

`:. -1 le (1+x^2)/(2x) le 1.`

`|1+x^2| le 2x`

`=>x^2-2|x| + 1 le 0`

`=>(|x| - 1)^2 le 0`

`=>|x| = 1`

`:. x = -1 or x = 1.`

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