If f(x)= a^x-a^ -x a^x+a^ -x , where a, x satisfy the necessary conditions, then f⁻¹(x)=

Step-by-step solution

aligned & y= a^x-a^ -x a^x+a^ -x = a^ 2 x -1 a^ 2 x +1 & y (a^ 2 x +1 )=a^ 2 x -1 & a^ 2 x = 1+y 1-y & x= 1 2 _a ( 1+y 1-y ) & f⁻¹(x)= 1 2 _a ( 1+x 1-x ) aligned