Published by:
CGP EDU Academic Team
Published on: August 14, 2026
The function f : R → R satisfies x + f(x) = f(f(x)) for every x ∈ R. Find all solutions of the equation
f(f(x)) = 0.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Notice that f(f(x)) – f(x) = x and if f(x) = f(y) then clearly x = y. This means that the function is injective. Since f(f(0)) = f(0) + 0 = f(0), because of injectivity we must have f(0) = 0, implying f(f(0)) = 0. If there were another x such that f(f(x)) = 0 = f(f(0)), injectivity would imply f(x) = f(0) and x = 0.
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