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JEE MainMathematicsInverse Trigonometric Functions

The number of integer values of x in the interval [0, 2 ] that satisfy the inequality ⁻¹( x) > ⁻¹( x) is

Options

  1. A4
  2. B6
  3. C5
  4. D7

Correct answer

C. 5

Step-by-step solution

Let f(x) = ⁻¹( x) and g(x) = ⁻¹( x) . We need to find the number of integers x [0, 2 ] such that f(x) > g(x) . We analyse the inequality in different sub-intervals of [0, 2 ] : For x [0, 2 ] , f(x) = x and g(x) = x . Thus, f(x) = g(x) . For x ( 2 , ] , f(x) = x and g(x) = - x . Since x > 2 , x > - x , so f(x) > g(x) . For x ( , 3 2 ] , f(x) = 2 - x and g(x) = - x . Clearly, 2 - x > - x , so f(x) > g(x) . For x ( 3 2 , 2 ) , f(x) = 2 - x and g(x) = x - 2 . Since x 0 and x - 2 g(x) . For x = 2 , f(2 ) = 0 and g(2 ) =

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