How do you find the inverse of #f(x)= (100)/(1+2^-x)#?

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Answer 1 · 2015-12-17T16:11:47

#y=-log_2((100-x)/x)#

Rewrite as

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

Flip the #x# and #y# and solve for #y#.

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

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

#1+2^-y=100/x#

#2^-y=100/x-1#

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

#-y=log_2((100-x)/x)#

#y=-log_2((100-x)/x)#

The graphs should be reflections of themselves over the line #y=x#.