Question

If $f\left(x\right)=\frac{1}{1-x},$ the the point of discontinuity of the function $f\left[f\right\{f\left(x\right)\left\}\right]$ is /are

• A. $\{0,-1\}$
• B. $\{0,1\}$
• C. $\{1,-1\}$
• D. None of these

Answer 1

Answer: (D)

None of these

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

Now, $f\left[f\left\{f\right(x\left)\right\}\right]=\frac{1-\frac{1}{1-x}}{-\frac{1}{1-x}}=\frac{\frac{1-x-1}{1-x}}{-\frac{1}{1-x}}=\frac{-x}{-1}=x$

Now, $f\left[f\left\{f\right(x\left)\right\}\right]=x$ is continuous everywhere