The function f is defined as #f(x) = x/(x-1)#, how do you find #f(f(x))#?

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Answer 1 · 2017-04-08T20:36:29

Substitute f(x) for every x and then simplify.

Given: #f(x) = x/(x-1)#

Substitute f(x) for every x

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

Multiply numerator and denominator by 1 in the form of #(x-1)/(x-1)#

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

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

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

#f(f(x)) = x#

This means that #f(x) = x/(x-1)# is its own inverse.