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`
or `|1+x^(2)| le |2x|, " for all " x`
or `1+x^(2) le |2x|, " for all " x " (As " 1+x^(2) gt 0`)
or `x^(2) -2|x|+1 le 0`
or ` |x|^(2) -2|x|+1 le 0 " (As " x^(2)=|x^(2)|`)
or `(|x|-1)^(2) le 0`
But `(|x|-1)^(2)` is always either positive or zero.
Thus, `(|x|-1)^(2)=0 " or " |x|=+-1`
Thus, the domain for f(x) is `{-1,1}.`