Mark (√) against the correct answer in the following:

Question:

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:

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

$\Rightarrow(f \circ f \circ f)(x)=f(f(f(x)))$

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

$\Rightarrow \mathrm{f}(\mathrm{f}(\mathrm{f}(\mathrm{x})))=\frac{1}{1-\mathrm{f}(\mathrm{f}(\mathrm{x}))}=\frac{1}{1-\left(1-\frac{1}{\mathrm{x}}\right)}=\frac{1}{\frac{1}{\mathrm{x}}}=\mathrm{x}$

 

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