Passage \( \quad: \) Let us define here three functions in the domain of \( [-1,1], f(x)=\sin ^{... VIDEO
Passage \( \quad: \) Let us define here three functions in the domain of \( [-1,1], f(x)=\sin ^{-1} x, g(x)=\cos ^{-1} x \)
Now another function
\[
\begin{array}{l}
I(x)=\max .\{f(x), g(x)\},-1 \leq x \leq 1 \\
J(x)=\min \{f(x), g(x)\},-1 \leq x \leq 1
\end{array}
\]
On the basis of above passage, answer the following questions :
Find the range of \( J(x) \)
(a) \( \left[-\frac{\pi}{2}, 0\right] \)
(b) \( \left[-\frac{\pi}{2}, \frac{\pi}{4}\right] \)
(c) \( \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \)
(d) None of these
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