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

1 Answer
Mar 31, 2016

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

Explanation:

Where ever you see #x# replace it with #1/(x-2)#

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

#color(blue)("Consider just the denominator")#

Multiply the 2 by #1# but in the form of #1-(x-2)/(x-2)#

So the denominator becomes

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

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

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

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

#color(blue)("Substitute into original expression")#

#color(green)(f(f(x))= 1 -: (2x+5)/(x-2)" "=" "(x-2)/(2x+5))#