Given #f(x)=1/(x-2)#, how do you find f(f^-1(x))?

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Answer 1 · 2016-03-09T14:59:31

First we must find the inverse.

The inverse can be found algebraically by switching y with x and vice versa.

#y = 1/(x - 2)#

#x = 1/(y - 2)#

#x(y - 2) = 1#

#y - 2 = 1/x#

#y = 1/x + 2#

We must now plug this into function ƒ, as the notation #ƒ(ƒ^-1(x))# denotes.\

#ƒ(x) = 1/(1/x + 2)#

So, #ƒ(ƒ^-1(x)) = 1/(1/x + 2)#