If f(x) = 1 1 - x , then the derivative of the composite function… - Vidyadip

Question

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

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Answer

c
(c) $f(x) = \frac{1}{{1 - x}}$ ==> $f\{ f(x)\} = \frac{{1 - x}}{{ - x}}$

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

$\therefore $ Derivative of $f[f\{ f(x)\} ] = 1$.

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