Question

Find the formula for the inverse of the function

y =(e^x) / (1+8e^x)

Answer 1

to form the inverse , we interchange the x and y variables, so the inverse equation is

x = e^y/(1+8e^y)
now we have to solve that for y ....

e^y = x + 8x e^y
e^y - 8x e^y = x
e^y( 1 - 8x) = x
e^y = x/(1-8x)

y = ln(x/(1-8x) or lnx - ln(1-8x)

Answer 2

dada