What is the inverse of #f(x) = (x+1)/(2x+1)#?

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Answer 1 · 2015-06-06T16:56:30

#f(x) = (x+1)/(2x+1) = (2(x+1))/(2(2x+1))#

#=((2x+1)+1)/(2(2x+1))#

#=1/2+1/(4x+2)#

Subtract #1/2# from both sides to get:

#1/(4x+2) = f(x)-1/2#

Take the reciprocal of both sides to get:

#4x+2 = 1/(f(x)-1/2)#

Subtract #2# from both sides to get:

#4x = 1/(f(x)-1/2) - 2#

Divide both sides by #4# to get:

#x=1/(4(f(x)-1/2)) - 2#

#=1/(4f(x)-2) - 2#

So

#f^-1(y) = 1/(4y-2) - 2#