Let f : R → R be a function such that f(x + y) = f(x) + f(y…

Maths Functions, Limits, Continuity and Differentiability JEE (Advamced) / IIT - JEE Problems ( Previous Year ) More Than One Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Let f : R → R be a function such that f(x + y) = f(x) + f(y), ∀ x, y ∈ R . If f(x) is differentiable at x = 0, then

f(x) is differentiable only in a finite interval containing zero

f(x) is continuous ∀ x ∈ R

f ′ (x) is constant ∀ x ∈ R

f(x) is differentiable except at finitely many points

Text Solution

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The correct answer is:

CHECK THE SOLUTION.

(b,c)

Sol. f(x) = kx

Hence f(x) is continuous & differentiable at x ∈ R & f ’ (x) = k (constant)

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