If f(x+y) = f(x) + f(y) for all x, y R (set of real numbers) and f(x) is continuous at x = 0, then identify the correct statement ? Option 1: f(x) is continuous for all x Option 2: f(x) is discontinuous at all x except \0\. Option 3: f(x) is continuous only at R^+ (set of positive real numbers) Option 4: f(x) is continuous only at R^- (set of negative real numbers)

The answer is 'f(x) is continuous for all x'. View full solution:

CUET Mathematics - If f(x+y) = f(x) + f(y) for all x, y R (set of real numbers) and f(x) is continuous at x = 0, then identify the correct statement ? | PYQs + Solutions

CUET Mathematics 2026 19th May Shift 2

Calculus

Hard

core

$f(x)$ is continuous for all $x$

$f(x)$ is discontinuous at all $x$ except $\{0\}$ .

$f(x)$ is continuous only at $R^+$ (set of positive real numbers)

$f(x)$ is continuous only at $R^-$ (set of negative real numbers)

✅ Correct Option: 1