Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If f(x) = 
n (x 1/n – 1) for x > 0 then which of the following is (are) true?
A
f(1/x) = 0
B
f(1/x) = 
C
f(1/x) = – f(x)
D
f(xy) = f(x) + f(y)
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(c, d)
f(x) = 
n (x 1/n – 1) ∀ x > 0
f(1/x) = 
n 
f(x) + f(1/x) = 
n 
∀ x > 0
f(x) + f(1/x) = 
f(x) + f(1/x) = 
∀ x > 0
f(x) + f(1/x) = {lnx – ln(x)} = 0 ∀ x > 0
f(x) = 
n(x 1/n – 1) = 
= lnx
f(y) = 
n (y 1/n – 1) = 
= lny
f(xy) = 
n[(xy) 1/n – 1]
f(xy) = 
⇒ log xy ⇒ lnx + lny
f(xy) = f(x) + (y)
∴ Option and are correct.
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