If ( h ⁻¹(x+i y)= 1 2 h ⁻¹ ( 2 x 1+x^2+y^2 )+ i 2 ⁻¹ ( 2 y 1-x^2-y^2 ) ), where (x, y R ), then ( h ⁻¹(i y)= )

Step-by-step solution

We have, ( h ⁻¹(x)= 1 i ⁻¹(i x) ) Put, ( x=i y ), we get ( h ⁻¹(i y)= 1 i ⁻¹(-y)= -1 i ⁻¹(y)=i ⁻¹(y) ) Hence, option (c) is correct.