# Get Answers to all your Questions

#### Explain solution RD Sharma class 12 chapter 8 Continuity exercise multiple choice question 28 maths

The correct option is (b)

Hint:

If a function f  is continuous at x = a then

$\lim _{x \rightarrow 0^{-}} f(a)=\lim _{x \rightarrow 0^{+}} f(x)=f(a)$

Given:

The function

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

Step 1: Understand that

$\{f: R-\{1\} \rightarrow R\}$

\begin{aligned} &\text { Therefore } f(f(x))=f\left(\frac{x-1}{x}\right) \\ &\begin{array}{c} f(f(x))=f\left(\frac{1}{1-\left(\frac{1}{x-1}\right)}\right) \\ \\=\frac{x-1}{x} \end{array} \end{aligned}

$\text { Step 2: Understand that } \therefore f \circ f: R-\{0,1\} \rightarrow R$

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

\begin{aligned} &f(f(f(x)))=f\left(\frac{x-1}{1-\left(\frac{x-1}{x}\right)}\right) \\ &=x \end{aligned}

\begin{aligned} &\text { Step 3: Understand that } \therefore f \circ f \circ f: R-\{0,1\} \rightarrow R \\ &\text { Therefore, } f(f(f(x))) \text { is not defined at } x=0,1 \\ &\text { Hence, } f(f(f(x))) \text { is discontinuous at } \{0,1\} \\ &\text { The set of point discontinuous of the function } f(f(f(x))) \text { is }\{0,1\} \end{aligned}

Hence, the correct answer is option (b)