The range of $$fx=$$$$sin$$$$-1x2+1x2+2$$ is

Here, $$x2+1x2+2=1-1x2+2$$ Now, $$2$$≤$$x2+2$$ $$0or$$ $$-12$$≤$$-1x2+2$$<$$0or$$ $$12$$≤$$1-1x2+2$$<$$1or$$ π$$6$$≤$$sin$$$$-11-1x2+2$$<π$$2$$

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The range of $f (x) = \sin^{- 1} (\frac{x^{2} + 1}{x^{2} + 2})$ is

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0, π6

π6, π2

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Correct option is C

Here, x2+1x2+2=1-1x2+2 Now, 2≤x2+2<∞ for all x∈Ror 12≥1x2+2>0or -12≤-1x2+2<0or 12≤1-1x2+2<1or π6≤sin-11-1x2+2<π2

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The range of fx=sin-1x2+1x2+2 is

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The range of $f (x) = \sin^{- 1} (\frac{x^{2} + 1}{x^{2} + 2})$ is