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NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

Let f x = s i n - 1 x 1 - x - x 1 - x 2 ,   ∀ 0 ≤ x ≤ 1 , then f x is

Options

  1. Anegative
  2. Bpositive
  3. Cnon-negative
  4. Dnon-positive

Correct answer

D. non-positive

Step-by-step solution

f x = s i n - 1 x 1 - x 2 - x 1 - x 2 ∵   s i n - 1 a - s i n - 1 b = s i n - 1 a 1 - b 2 - b 1 - a 2 ⇒ f x = sin - 1 x - sin - 1 x ≤ 0   as   x ≤ x

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