If `f(x) = sin^(-1) x` then prove that `lim_(x rarr (1^(+))/(2)) f(3x -4x^(3)) = pi - 3 lim_(x rarr (1^(+))/(2)) sin^(-1) x`

Explanation

`sin^(-1) (3x -4x^(3)) = pi - 3 sin^(-1) x " if " (1)/(2) lt x lt 1`
`:. underset(x rarr (1)/(2))("lim") f(3x - 4x^(3)) = underset(x rarr (1)/(2))("lim") (pi - 3 sin^(-1) x)`
`= pi - 3 underset(x rarr (1)/(2))("lim") sin^(-1) x`