Function f(x) = x/(x + 1): Find f(f(x)) (how to solve?)

[celebrityrose000]

Let f(x) = x/(x+1)

Then f(f(x)) = _______ / _________

ok so I set it up as

(x/(x+1))/((x/(x+1))+1)

but from here on out I'm confused about how to solve it. Do I multiply the denominator "x+1" to the top (the x)? I'm confused about how to solve this

 

[Loren]

Re: Functions

(x/(x+1))/((x/(x+1))+1) means
\(\displaystyle \frac{\frac{x}{x+1}}{\frac{x}{x+1}+1}\)

There are different approaches. I would combine the fractions in the denominator first getting...

\(\displaystyle \frac{\frac{x}{x+1}}{\frac{x+x+1}{x+1}}\)

I would then simplify the denominator. Following that I would multiply numerator and denominator of the big fraction by x+1. Then, go from there.

 

[Deleted member 4993]

Re: Functions

Let f(x) = x/(x+1)

Then f(f(x)) = _______ / _________

ok so I set it up as

(x/(x+1))/((x/(x+1))+1)

but from here on out I'm confused about how to solve it. Do I multiply the denominator "x+1" to the top (the x)? I'm confused about how to solve this

This is not an equation - no "equal to" sign - so nothing to solve!

You may simplify it...