The range of the function f x = s i n - 1 x 2 1 + x 2 , x ∈ R is

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The range of the function

f (x) = s i n^{- 1} (\frac{x^{2}}{1 + x^{2}}), x \in R

is

MathematicsInverse Trigonometric FunctionsJEE Main

Options:

A $[\frac{- π}{2}, \frac{π}{2}]$
B $[0, \frac{π}{2})$
C $(0, \frac{π}{2}]$
D $(\frac{- π}{2}, \frac{π}{2})$

Solution:

2442 Upvotes Verified Answer

The correct answer is:

[0, \frac{π}{2})

\frac{x^{2}}{1 + x^{2}} = 1 - \frac{1}{1 + x^{2}} \in [0,1)

∴

Range of

f (x) \in [s i n^{- 1} (0), s i n^{- 1} (1))

\in [0, \frac{π}{2})

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