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

To prove that

\[ \lim_{x \to \frac{1^{+}}{2}} f(3x - 4x^3) = \pi - 3 \lim_{x \to \frac{1^{+}}{2}} \sin^{-1} x \]

where \( f(x) = \sin^{-1} x \), we can follow these steps:

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