If f(x × f(y)) = ∀ x, y ∈ R , y ≠ 0, then prove that f(x) …

Maths Functions, Limits, Continuity and Differentiability General Subjective Type

Published on: August 13, 2026

If f(x × f(y)) = ∀ x, y ∈ R , y ≠ 0, then prove that f(x) . f = 1

Text Solution

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The correct answer is:

CHECK THE SOLUTION.

(i) Put x = y = 1 in given relation, we get f(f(1)) = f(1)

(ii) Now put x = 1, y = f(1) in given relation, we get f(f(1)) = = 1

from (i) and (ii)

∴ f(f(1)) = 1

∴ f(1) = 1

Put x = 1, f(f(y)) = ⇒ f(f(y)) = now substitute y = f(x)

f(f(f(x))) = ⇒ =

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