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

1 Answer
Jul 28, 2016

#f(f(x))=(x-2)/(5-2x)#

Explanation:

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

Now to find #f(f(x))# we have to just substitute #f(x)# in place of #x#. As #f(x)=1/(x-2)#, to find #f(f(x))#, we substitute #1/(x-2)# in place of #x# on Right Hand Side, Hence

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

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

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

= #1/((5-2x)/(x-2))#

= #(x-2)/(5-2x)#