Question

If f (x)= 1÷(1-x) then find f (f (f (x)))

Answer 1

Question :-

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

Answer :-

$\implies \red{\boxed{\sf{f(f(f(x))) = x}} }\:$

Explanation :-

$\implies \sf{ f(x) = \frac{1}{1 - x} } \\ \\ \rightarrow \sf{ f(f(x)) = \frac{1}{1 - \frac{1}{1 - x} } } \\ \\ \rightarrow \sf{f(f(x)) = \frac{1}{ \frac{1 - x - 1}{1 - x} } } \\ \\ \rightarrow \sf{f(f(x)) = \frac{1 - x}{ - x} } \\ \\ \rightarrow \: \sf{f(f(f(x))) = \frac{1}{1 - \frac{1 - x}{ - x} } } \\ \\ \rightarrow \sf{ f(f(f(x))) = \frac{1}{ \frac{ - x - 1 + x}{ - x} } } \\ \\ \rightarrow \sf{f(f(f(x))) = \frac{ - x}{ - 1} } \\ \\ \rightarrow \boxed{\sf{f(f(f(x))) = x}}$