Question

if f(x)=x/1-x,then f[f[f(x)]]=??

Answer 1

f(x) =  x/ (1-x)     , x ≠1

$f( f(x) ) = \frac{\frac{x}{1-x}}{1-\frac{x}{1-x}}=\frac{x}{1-2x}\\\\f(f(f(x)))=\frac{\frac{x}{1-2x}}{1-\frac{x}{1-2x}}=\frac{x}{1-3x}$

Answer 2

Question:

$if \: f(x) \: = \frac{x}{1 - x} \: then \: find \: f(f(f(x)))$

Answer:

Need to find f(f(f(x))) Hence solve step by step of reducing the functions of x one by one

Here ,

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

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

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

$f(f(x)) = \frac{x}{1 - 2x}$

Now Substitute The value of f(f(x)) in f(f(f(x))),

$f(f(f(x))) = \frac{ \frac{x}{1 - 2x} }{1 - \frac{ x}{1 - 2x} }$

$f(f(f(x))) = \frac{ \frac{x}{(1 - 2x)} }{ \frac{(1 - 2x) - x}{(1 - 2x)} }$

$f(f(f(x))) = \frac{x}{1 - 3x}$

Be Delighted :)