Question

what is the inverse function of f(x)=(e^x)/1+8e^x

Answer 1

flip x and y
\[x = \frac{e^y}{1+8e^y}\]
\[e^y = x + 8x e^y\]
\[e^y (1-8x) = x\]
\[e^y = \frac{x}{1-8x}\]
\[y = \ln (\frac{x}{1-8x})\]
For x>0 , x not equal 1/8