Let \( f_{n}(x)=(\sin x)^{1 / n}+(\cos x)^{1 / n}, x \in R \), then :
(a) \( f_{2}(x)1 \) for al... VIDEO
Let \( f_{n}(x)=(\sin x)^{1 / n}+(\cos x)^{1 / n}, x \in R \), then :
(a) \( f_{2}(x)1 \) for all \( x \in\left(2 k \pi(4 k+1) \frac{\pi}{2}\right), k \in I \)
(b) \( f_{2}(x)=1 \) for \( x=2 k \pi, k \in I \)
(c) \( f_{2}(x)f_{3}(x) \) for all \( x \in\left(2 k \pi,(4 k+1) \frac{\pi}{2}\right), k \in I \)
(d) \( f_{3}(x) \geq f_{5}(x) \) for all \( x \in\left(2 k \pi,(4 k+1) \frac{\pi}{2}\right), k \in I \)
(Where \( I \) denotes set of integers)
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