Can this disappear like this?

Algebra Level 2

Let $f(x)$ be a function defined as $f(x)=1/(1-x)$

What is the value of $f(f(f(x)))$ .

x

\frac1x

\frac1{1-x}

1-x

2 solutions

Kshitij Johary
Jun 7, 2014

If $f(x) = \frac{1}{1-x}$ , then $(f(f(x))) = \frac{1}{1- (\frac{1}{1-x})}$ Solving this we get,

$(f(f(x))) = \frac{1-x}{-x}$

Again replacing this with $x$ in $f(x)$ , we get,

$f(f(f(x))) = \frac{1}{1-(\frac{1-x}{-x})}$

Ultimately, solving this will fetch the answer which is $\boxed {f(f(f(x))) = x}$

Yeah that's a good one dude

ashutosh mahapatra - 7 years ago

Ashutosh Mahapatra
Jun 3, 2014

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