Question

If $f\left(x\right)=\frac{x}{x-1}$, then $\frac{\left(fofo........of\right)\left(x\right)}{19times}$ is equal to :

• A. $\frac{x}{x-1}$
• B. ${\left(\frac{x}{x-1}\right)}^{19}$
• C. $\frac{19x}{x-1}$
• D. $x$

Answer 1

Answer: (A)

Given $f\left(x\right)=\frac{x}{x-1}$
$\therefore \left(fof\right)\left(x\right)=ff\left(x\right)=f\left(\frac{x}{x-1}\right)$
$=\frac{\frac{x}{x-1}}{\frac{x}{x-1}-1}=\frac{\frac{x}{x-1}}{\frac{x-x+1}{x-1}}=\frac{\frac{x}{x-1}}{\frac{1}{x-1}}=x$.
$\Rightarrow \left(fofof\right)\left(x\right)f\left(fof\right)\left(x\right)f\left(x\right)=\frac{x}{x-1}$
$\Rightarrow \underbrace{\left(fofof.....of\right)}\left(x\right)=f\left(fof\right)\left(x\right)=f\left(x\right)=\frac{x}{x-1}$
19 times