Question

函数f(x)=(3的x次幂-1)/(3的x次幂+1)(X属于R)的反函数为

Answer 1

y=(3^x-1)/(3^x+1)

3^x-1=y*3^x+y

3^x(1-y)=1+y

3^x=(1+y)/(1-y)

x=log3[(1+y)/(1-y)]

反函数为

y=log3[(1+x)/(1-x)] -1