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

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a

0,π2

b

0,π2

c

0,π2

d

None of these

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detailed solution

Correct option is B

Clearly, for y to be defined, x21+x2≤1 which is true for all x ∈ R. So, the domain = (– ∞, ∞). Now, y=sin−1⁡x21+x2⇒x21+x2=sin⁡y ⇒x=x21+x2For x to be real, sin y ≥ 0 and 1 – sin y > 0⇒0≤sin⁡y<1⇒y∈0,π2∴ Range =0,π2

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