Consider the function #f(x)=1/(x-2)#, then how do you simplify #f(f^-1(x))#?

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Answer 1 · 2016-08-19T20:25:29

#f^{-1}(x) = 1/x+2# and
#f(f^{-1}(x) ) = x#

Given #f(x) = 1/(x-2)# then

#f(g(x)) = 1/(g(x)-2)#. Now, if #f(g(x)) = x# then

#g(x) = f^{-1}(x)#

but

# 1/(g(x)-2)=x# gives #g(x) = 1/x+2#

then

#f^{-1}(x) = 1/x+2#