Question
Question: Let f(x) be defined for all x \> 0 and be continuous. Let f(x) satisfy f(x/y) = f(x) – f(y) for all ...
Let f(x) be defined for all x > 0 and be continuous. Let f(x) satisfy f(x/y) = f(x) – f(y) for all x, y and f(5) = 1. Then
A
f(x) is bounded
B
f(1/x) → 0 as x → 0
C
x f(x) → 1 as x → 0
D
f(x) = ln x
Answer
f(x) = ln x
Explanation
Solution
f(x) is continuous “x > 0 and f(x/y) = f(x) – f(y)
Also f(5) = 1
⇒ Clearly f(x) = ln x satisfies all these properties.× f(x) = ln x