How do you find the inverse function of #f(x)=x/(x+1)#?

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Answer 1 · 2015-10-31T23:32:21

Let #y = f(x)# and rearrange to find an expression for #x# in terms of #y#, hence:

#f^-1(y) = y/(1-y)#

Let #y = f(x) = x/(x+1) = (x+1-1)/(x+1) = 1-1/(x+1)#

Then:

#1-y = 1/(x+1)#

Hence:

#1/(1-y) = x+1#

Hence:

#x = 1/(1-y)-1 = (1-(1-y))/(1-y) = y/(1-y)#

So #f^-1(y) = y/(1-y)#