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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NTA Abhyas 2020 · Mathematics · Inverse Trigonometric Functions

The range of the function f(x) = sin^ - 1 ( x^ 2 1 + x^ 2 ), x ∈ ℝ...

The range of the function f(x)=sin−1(x21+x2),x∈Rf\left(x\right) = sin^{- 1}\left(\dfrac{x^{2}}{1 + x^{2}}\right), x \in \mathbb{R} is

Options

  1. A[−π2,π2]\left[\dfrac{- \pi}{2}, \dfrac{\pi}{2}\right]
  2. B[0,π2)\left[0, \dfrac{\pi}{2}\right)
  3. C(0,π2]\left(0, \dfrac{\pi}{2}\right]
  4. D(−π2,π2)\left(\dfrac{- \pi}{2}, \dfrac{\pi}{2}\right)

Correct answer

B. [0,π2)\left[0, \dfrac{\pi}{2}\right)

Step-by-step solution

x21+x2=1−11+x2∈[0,1)∴\dfrac{x^{2}}{1 + x^{2}} =1 - \dfrac{1}{1 + x^{2}} \in \left[0,1\right) ∴ Range of f \left(x\right)\in \left[sin^{- 1} \left(0\right), sin^{- 1} \left(1\right)\right)∈[0,π2)∈ \left[0, \dfrac{\pi}{2}\right)
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