Find the inverse of the following functions
(i) \( f(x)=\sin ^{-1}\left(\frac{x}{3}\right), x \i...
Find the inverse of the following functions
(i) \( f(x)=\sin ^{-1}\left(\frac{x}{3}\right), x \in[-3,3] \)
(ii) \( f(x)=\log _{\theta}\left(x^{2}+3 x+1\right), x \in[1,3] \)
(iii) \( f(x)=5^{\log _{0} x}, x0 \)
(iv) \( f(x)=\log _{\theta}\left(x+\sqrt{x^{2}+1}\right) \)
(v) \( f(x)=\left\{\begin{array}{ll}x, & x1 \\ x^{2}, & 1 \leq x \leq 4 \\ 8 \sqrt{x}, & x4\end{array}\right. \)
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