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

Explanation

`f(x) = sin^(-1) ((1 + x^(2))/(2x))` is defined for `- 1 le (1 + x^(2))/(2x) le 1 " or " |(1 + x^(2))/(2x)| le 1`
`rArr |1 + x^(2) | le | 2x|`, for all x
`rArr 1 + x^(2) le | 2x|`, for all x (as `1 + x^(2) gt 0`)
`x^(2) - 2|x| + 1 le 0`
`rArr |x|^(2) - 2|x| + 1 le 0` (as `x^(2) = |x|^(2)`)
But `(|x| - 1)^(2)` is always either positive or zero. Thus,
`(|x| -1)^(2) = 0`
or `|x| = 1 " or " x = +- 1`
Hence, domain for `f(x) " is " {-1, 1}`