Question

If $f(x)=\frac{1}{1-x},$ then the derivative of the composite function f[f{(f (x))}] is equal to:

• A. 0
• B. $\frac{1}{2}$
• C. 1
• D. 2

Answer 1

Answer: (C)

$f(x)=\frac{1}{1-x}\Rightarrow f\{f(x)\}=\frac{1-x}{-x}$
$\Rightarrow f[f\{f(x)\}]=\frac{-x}{-x-1+x}=x$
$\therefore$ Required derivative = 1