Inverse problem help!!?

Question

f(x)= 100/1+2^-x


find the inverse

Answer 1

y=100/[1+2^(-x)]

1+ 2^(-x) = 100/y

2^(-x) = 100/y -1

-x = log[ (100-y)/y] / log2

x= [log(y) -log(100-y)] / log 2

f^(-1) (x) = Log_{base 2} (x) - Log_{base2} (100-x)

when x is in (0, 100)

Saludos.

Answer 2

f(x) = y = 100/(1 + 2^-x)
interchange x and y and resolve for y:

x = 100/(1 + 2^-y)
1 + 2^-y = 100/x
2^-y = 100/x - 1
-y log 2 = log( 100/x - 1)
y = -log(100/x -1)/log(2)

that's assuming I put the () in the place you meant in the 1st step.

Answer 3

y = 100/(1 + 2^(-x))
1 + 2^(-x) = 100/y
2^(-x) = (100 - y)/y
2^x = y/(100 - y)
x(ln2) = ln[y/(100 - y)]
x = (1/ln2) * ln[y/(100 - y)] ---> f^-1(y)
y = (1/ln2) * ln[x/(100 - x)] ---> f^-1(x)