Mark (√) against the correct answer in the following:If \(f(x)=\fra

1.	Mark (√) against the correct answer in the following:If \(f(x)=\frac{1}{(1-x)}\) then (f o f o f) (x) = ?\(A.\frac{1}{1-3x}\) \(B.\frac{x}{1+3x}\)C. xD. None of these
Answer» Correct Answer is (C) x \(f(x)=\frac{1}{1-x}\) \(\Rightarrow (fofof)(x)=f(f(f(x)))\) \(\Rightarrow f(f(x))=\frac{1}{1-f(x)}\)\(=\frac{1}{1-\frac{1}{1-x}}\)\(=\frac{1-x}{1-x-1}\)\(=\frac{x-1}{x}\)\(=1-\frac{1}{x}\) \(\Rightarrow f(f(f(x)))=\frac{1}{1-f(f(x))}\)\(=\frac{1}{1-(1-\frac{1}{x})}\)\(=\frac{1}{\frac{1}{x}}\)= x

Mark (√) against the correct answer in the following:If \(f(x)=\frac{1}{(1-x)}\) then (f o f o f) (x) = ?\(A.\frac{1}{1-3x}\) \(B.\frac{x}{1+3x}\)C. xD. None of these

Answer»

Correct Answer is (C) x

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

\(\Rightarrow (fofof)(x)=f(f(f(x)))\)

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

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