Q.
If $f(x) = \frac{x}{x - 1},\ x \neq 1$ then
is equal to
A) $\frac{x}{x - 1}$
B) ${\left( \frac{x}{x - 1} \right)\ }^{19}$
C) $\frac{19x}{x - 1}$
D) $x$
Explanation
(a)
$(fof)x = f\left( \frac{x}{x - 1} \right)$
$\ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{\frac{x}{x - 1}}{\left( \frac{x}{x - 1} \right) - 1} = x$
$\Rightarrow \ \ \ \ \ \ \ \ \ (fofof)x = f(fof)x = f(x) = \frac{x}{x - 1}$
$\therefore\ \ \ \ \ \ \ (fofof\ldots 19\ times)(x) = \frac{x}{x - 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.