Functions Question 718
Question: If $ f(x)=\frac{x}{x-1}, $ then $ \frac{(fofo…of)(x)}{19times} $ is equal to:
Options:
A) $ \frac{x}{x-1} $
B) $ {{( \frac{x}{x-1} )}^{19}} $
C) $ \frac{19x}{x-1} $
D) x
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ \because f(x)=\frac{x}{x-1} $
$ \therefore (fof)(x)=f{f(x)}=f( \frac{x}{x-1} ) $ $ =\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 (fofof)(x)=f(fof)(x)=f(x)=\frac{x}{x-1} $
$ \Rightarrow \underbrace{(fofof….of)}_{19,times}(x)=f(fof)(x)=f(x)=\frac{x}{x-1} $
BETA
