Question

If $f\left(x\right)=\frac{1}{1-x},x\ne 1$ then $\left(fofof\right)\left(x\right)=$

• A. $x$
• B. $x^2$
• C. $x^3$
• D. $\frac{1}{x}$

Answer 1

Answer: (A)

$x$

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

$fof=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}=\frac{x-1}{x}$

Now,

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