Let f : R → R be a function such that f ( x + y ) = f ( x ) + f ( y ), ∀ x , y ∈ R . If f…
Mathematics · JEE Advanced · NTA Exams — Sets, Relations and Functions
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 + 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
- f
- f(x) is differentiable except at finitely many points
Answer
(B) f ( x ) is continuous ∀ x ∈ R
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