Most Important Selected Qs for JEE AdvancedMathematicsInverse Trigonometric Functions

Let f(x)= ⁻¹ ( 2 x 1+x^2 ), g(x)= ⁻¹ ( 1-x^2 1+x^2 ) and h(x)= ⁻¹ ( 2 x 1-x^2 ) , then:

Options

Af(x)+2 ⁻¹ x= x 1
Bf(x) g(x) =1 x [0,1]
Cg(x)+h(x)= x (-1,0)
D_ x 1⁺ (f(x)+g(x)+h(x)) _ x 1⁻ (f(x)+g(x)+h(x)) =3

Correct answer

C. g(x)+h(x)= x (-1,0)

Step-by-step solution

aligned & f(x)= ⁻¹ ( 2 x 1+x^2 )= cases 2 ^1 x, & -1 x 1 -2 ⁻¹ x, & x 1 - -2 ⁻¹ x, & x -1 cases & g(x)= ⁻¹ ( 1-x^2 1+x^2 )= cases 2 ⁻¹ x, & x 0 -2 ⁻¹ x, & x 1 cases aligned

Practice Inverse Trigonometric Functions on Quantrex Academy →

More from Inverse Trigonometric Functions

Considering only the principal values of the inverse trigonometric functions, the value of ⁻¹( (-11)) + 10 (2 ⁻¹ ( 1 2 ) ) + 10 (2 ⁻¹(2)) is 2026 Let = 3 ⁻¹ ( 6 11 ) and = 3 ⁻¹ ( 4 9 ) , where inverse trigonometric functions take only the principal values. Given below are two statements: Statement I: ( + ) > 0 . Statement II 2026 If ( ⁻¹(x 2 )) = ( ⁻¹ 1-x^2 ) , x (0,1) , then the value of x is : 2026 Let [ ] denote the greatest integer function. If the domain of the function f(x) = ⁻¹ ( x+[x] 3 ) is [ , ) , then ^2 + ^2 is equal to: 2026 Let 0 < < 1 , = 1 3 and ⁻¹(1- ) + ⁻¹(1- ) = 4 . Then 6( + ) is equal to: 2026 If 4 + _ p=1 ¹¹ ⁻¹ ( 2^ p-1 1 + 2^ 2p-1 ) = , then is equal to __________. 2026 If y = ⁻¹ ( 3 x - 4 x 4 x + 3 x ) + 2 ⁻¹ ( x 1+ 1-x^2 ) , then dy dx at x = 3 2 is equal to: 2026 Considering the principal values of inverse trigonometric functions, the value of the expression (2 ⁻¹ ( 2 13 )-2 ⁻¹ ( 3 10 ) ) is equal to : 2026 Full Inverse Trigonometric Functions list All Most Important Selected Qs for JEE Advanced PYQs