Functions Question 590
Question: If $ f(x)=\frac{\alpha x}{x+1},x\ne -1 $ , for what value of $ \alpha $ is $ f(f(x))=x $
[Kerala (Engg.) 2005]
Options:
A) $ \sqrt{2} $
B) $ -\sqrt{2} $
C) 1
D) 2
E) ?1
Show Answer
Answer:
Correct Answer: E
Solution:
$ f(x)=\frac{\alpha x}{x+1} $ ; $ f(f(x))=f( \frac{\alpha x}{x+1} )=\frac{\alpha ( \frac{\alpha x}{x+1} )}{\frac{\alpha x}{x+1}+1} $ But $ f(f(x))=x $ , \ $ \frac{{{\alpha }^{2}}x}{\alpha x+x+1}=x $ Put $ \alpha =-1 $ , $ \frac{{{(-1)}^{2}}x}{(-1)x+x+1}=\frac{x}{-x+x+1}=x $ ; \ $ \alpha =-1 $ .
BETA
