Question

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

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

$y=x$ is an equation of straight line.

Hence, 'C' is correct.