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

Home » Mark (√) against the correct answer in the following: If then (f of of) A. B. C. D. None of these

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

CBSE | Class 12 | Functions | Maths | RS Aggarwal

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

Solution:

Option(C) is correct.
$\mathrm{f}(\mathrm{x})=\frac{1}{(1-x)}$
According to the combination of $\mathrm{f}$ and $\mathrm{f}$ , fofof $(x)=f(f(f(x)))$
Therefore, fof $(x)=f(f(f(x))$
$\begin{array}{l} =\mathrm{f}\left(\mathrm { f } \left(\left(\frac{1}{(1-x)}\right)\right.\right. \\ =\mathrm{f}\left(\frac{1}{\left(1-\frac{1}{(1-x)}\right)}\right) \\ =\mathrm{f}\left(\frac{1-x}{1-x-1}\right) \\ =\mathrm{f}\left(1-\frac{1}{x}\right) \\ =\frac{1}{\left(1-\left(1-\frac{1}{x}\right)\right)}=\frac{1}{\frac{1}{x}}=\mathrm{x} \end{array}$