Let f(x)={sin⁡−1(sin⁡x),x>0π2,x=0cos⁡−1(cos⁡x),x<0f(x)=\begin{cases}\sin^{-1}(\sin x), & x>0\\ \frac{\pi}{2}, & x=0\\ \cos^{-1}(\cos x), & x<0\end{cases}…

Mathematics

Problem

Let f(x)={sin⁡−1(sin⁡x),x>0π2,x=0cos⁡−1(cos⁡x),x<0f(x)=\begin{cases}\sin^{-1}(\sin x), & x>0\\ \frac{\pi}{2}, & x=0\\ \cos^{-1}(\cos x), & x<0\end{cases} then (a) f(x)f(x) has local maxima at x=0x=0 (b) f(x)f(x) is continuous for all x∈Rx\in\mathbb{R} (c) f(x)f(x) has maximum value π\pi (d) f(x)f(x) has minimum value 0 (a) f(x)f(x) has local maxima at x=0x=0 (b) f(x)f(x) is continuous for all x∈Rx\in\mathbb{R} (c) f(x)f(x) has maximum value π\pi (d) f(x)f(x) has minimum value 0

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