Consider the following statements: 1. There exists (- 2 , 2 ) for which ⁻¹( ) . 2. ⁻¹ ( 1 3 )- ⁻¹ ( 1 5 )= ⁻¹ ( 2 2 ( 3 -1) 15 ) Which of the above statements is/are correct?

Step-by-step solution

(- 2 , 2 ) for which ⁻¹( )= Hence, statement (1) is incorrect. aligned & if x 1 ; y 1 & x^2+y^2 1 & ⁻¹(x)- ⁻¹ y = ⁻¹ [ x 1- y ^2 - y 1- x ^2 ] aligned aligned & ⁻¹ 1 3 - ⁻¹ 1 5 & = ⁻¹ [ 1 3 1- 1 25 - 1 5 1- 1 9 ] & = ⁻¹ [ 1 3 5 24 - 1 5 3 8 ] & = ⁻¹ [ 8 3 - 8 15 ]= ⁻¹ [ 2 2 ( 3 -1) 15 ] aligned Hence, statement (2) is correct.