Question

what is the inverse of this function?

Answer 1

\[f(x)=\log _{a}\frac{ x+1 }{ 1-x } \]

Answer 2

@ganeshie8 and @aum help me please.

Answer 3

@k142.

Answer 4

@campbell_st .

Answer 5

I think @aum just solved a question like this in a previous post. It is similar to that one.

Answer 6

\[
f(x)=\log _{a}\frac{ x+1 }{ 1-x } \\
y = \log _{a}\frac{ x+1 }{ 1-x } \\
x = \log _{a}\frac{ y+1 }{ 1-y } \\
a^x = \frac{ y+1 }{ 1-y } \\
a^x - a^xy = y + 1 \\
a^x - 1 = y + a^xy = y(1 + a^x) \\
y = \frac{a^x-1}{a^x+1} \\
f^{-1}(x) = \frac{a^x-1}{a^x+1}
\]