Find the domain of `f(x)(sqrt((1-sinx)))/((log)_5(1-4)^2)+cos^(-1)(1-{x})dot`

Answer

`(-1//2,1//2)-{0}`

Explanation

(a) `1-sinx ge 0 " or " sin x le 1 " or " x in R`
(b) ` 1-4x^(2) gt 0 " or " x in (-1//2,1//2)`
(c ) `log_(5)(1-4x^(2)) ne 0 " or " 1-4x^(2) ne 1 " or " x ne 0`
(d) `-1 le 1-{x} le 1 " or " 0 le {x} le 2 " or " x in R`
Hence, domain is common values of (a),(b),(c) and (d),
i.e., `x in (-(1)/(2),(1)/(2))-{0}`