Functions Question 636
Question: Let $ f(x) $ be defined for all $ x>0 $ and be continuous. Let $ f(x) $ satisfy $ f( \frac{x}{y} )=f(x)-f(y) $ for all x, y and $ f(e)=1, $ then
[IIT 1995]
Options:
A) $ f(x)=\ln x $
B) $ f(x) $ is bounded
C) $ f( \frac{1}{x} )\to 0 $ as $ x\to 0 $
D) $ x,f(x)\to 1 $ as $ x\to 0 $
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ f(x)= $ ln $ (x),x>0 $ $ f(x)= $ ln $ (x) $ is a continuous function of x for every positive value of x.
$ 0<x<1 $ ln $ ( \frac{x}{y} )= $ ln (x)? ln (y)=f(x)? f(y).
BETA
