Question

$f\left(x\right)=\frac{1}{(1-x)},x\ne 0,1,$ then the graph of the function $y=f(f(f\left(x\right)),x>1$ is

• A. a circle
• B. an ellipse
• C. a straight line
• D. a pair of straight lines

Answer 1

The correct option is C

a straight line

Explanation for the correct option:

Step 1. Find the value of $y=f(f(f\left(x\right)\left)\right)$:

$f\left(x\right)=\frac{1}{(1–x)}$

$f(f(x\left)\right)=\frac{1}{[1–f(x\left)\right]}$

$=\frac{1}{\left[1-{\displaystyle \frac{1}{(1-x)}}\right]}$

$=\frac{(1–x)}{(-x)}$

$=\frac{\left(x–1\right)}{x}$

Step 2. Put the value of $f(f(x\left)\right)$ in $y=f(f(f\left(x\right)\left)\right)$

$=\frac{1}{\left[1–{\displaystyle \frac{(x–1)}{x}}\right]}$

$=\frac{x}{\left(x–x+1\right)}$

$=x$

$\therefore$$y=x$is a straight line.

Hence, Option ‘C’ is Correct.