Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2018MathematicsInverse Trigonometric Functions

The value of [ ⁻ ( ⁻¹ x ) ] is

Options

  1. A( 1+x² 2+x² )
  2. B( 2+x² 1+x² )
  3. C( x²-2 x²-1 )
  4. D( x²-1 x²-2 )

Correct answer

A. ( 1+x² 2+x² )

Step-by-step solution

We have [ ⁻¹ ( ⁻¹ x ) ] Now, ( ⁻¹ x )= [ ⁻¹ 1 x²+1 ]= 1 x²+1 [ ( ⁻¹ x )=x, x [-1,1] ] So, ⁻¹ ( 1 x²+1 )= ⁻¹ ( x²+1 x²+2 ) Thus, [ ⁻¹ ( 1 x²+1 ) ]= [ ⁻¹ ( x²+1 x²+2 ) ]= (x²+1 ) x²+2 [ ( ⁻¹ x )=x, x [-1,1] .

Practice Inverse Trigonometric Functions on Quantrex Academy →

More from Inverse Trigonometric Functions

If y = ⁻¹ ( 1+x^3 + 1-x^3 1+x^3 - 1-x^3 ) then dy dx = 2026If X = ⁻¹ [2 (2 ⁻¹ 1 2 ) ] + ⁻¹ [ ( 7 6 ) ] and Y = ⁻¹ [ ( 11 6 ) ] + ⁻¹ [ ( 4 3 ) ] then the value of 2X - Y is: 2026The value of the expression ⁻¹ ( 7 6 ) + ⁻¹ ( 22 3 ) + ⁻¹ ( 4 5 ) is: 2026Which of the following is the simplest form of the expression ⁻¹ ( 1+x^2 - 1 x ) where x 0 2026If ⁻¹ x + ⁻¹ y = 2 , then x^2 is equal to 2026⁻¹ ( 1 1 + 1 2 ) + ⁻¹ ( 1 1 + 2 3 ) + + ⁻¹ ( 1 1 + n(n+1) ) = 2026The second order derivative of ⁻¹(4x^3 - 3x) with respect to ⁻¹(2x^2 - 1) , where 1 2 < x < 1 is 2026If 2 ⁻¹x - 3 ⁻¹x = 4 , then 2 ⁻¹x + 3 ⁻¹x = 2026 Full Inverse Trigonometric Functions list All COMEDK PYQs