If $$f\left( x \right) = \frac{1}{{1 - x}},\,x \ne 0,\,1,$$ then the graph of the function $$y = f\left\{ {f\left( {f\left( x \right)} \right)} \right\},\,x > 1,$$ is :
A.
a circle
B.
an ellipse
C.
a straight line
D.
a pair of straight lines
Answer :
a straight line
Solution :
$$\eqalign{
& f\left\{ {f\left( x \right)} \right\} = \frac{1}{{1 - f\left( x \right)}} = \frac{1}{{1 - \frac{1}{{1 - x}}}} = \frac{{1 - x}}{{ - x}} = \frac{{x - 1}}{x} \cr
& \therefore f\left\{ {f\left( {f\left( x \right)} \right)} \right\} = \frac{1}{{1 - f\left\{ {f\left( x \right)} \right\}}} = \frac{1}{{1 - \frac{{x - 1}}{x}}} = x \cr
& \therefore {\text{ the graph has the equation }}y = x \cr} $$
Releted MCQ Question on Calculus >> Function
Releted Question 1
Let $$R$$ be the set of real numbers. If $$f:R \to R$$ is a function defined by $$f\left( x \right) = {x^2},$$ then $$f$$ is: