SOLUTION: LET {{{F(X)=X/(X+1)}}} THEN F(F(X))= ?/X^2+2X+1

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: LET {{{F(X)=X/(X+1)}}} THEN F(F(X))= ?/X^2+2X+1      Log On


   

Question 18861: LET F%28X%29=X%2F%28X%2B1%29 THEN F(F(X))= ?/X^2+2X+1
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=x/(x+1)
then
f(f(x))=%28x%2F%28x%2B1%29%29%2F%28%28x%2F%28x%2B1%29%29%2B1%29
=%28x%2F%28x%2B1%29%29%2F%28%28x%2Bx%2B1%29%2F%28x%2B1%29%29
=x%2F%282x%2B1%29..this is what it is ...but if it is to be written as
?/(x^2+2x+1)or shall we say y/(x^2+x+1)...then we have
y/(x^2+2x+1)=x/(2x+1)..so
y=(x^2+2x+1)*x/(2x+1)