Question:medium
Let f:RtoR be a function such that f(x+y)=f(x)+f(y).
If f(x) is differentiable at x=0, then which one of the following is incorrect?
Let f:RtoR be a function such that f(x+y)=f(x)+f(y).
If f(x) is differentiable at x=0, then which one of the following is incorrect?
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Cauchy functional equation + differentiability ⟹ linear function.
Updated On: Mar 20, 2026
- \(f(x)\) is continuous, \(\forall x\in\mathbb{R}\)
- \(f'(x)\) is constant, \(\forall x\in\mathbb{R}\)
- \(f(x)\) is differentiable, \(\forall x\in\mathbb{R}\)
- f(x) is differentiable only in a finite interval containing zero
Show Solution
The Correct Option is D
Solution and Explanation
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