Let g(x) be a function such that g(a + b) = g(a). g(b) ∀ a,…

Maths Functions, Limits, Continuity and Differentiability General Numeric Response

Published on: August 13, 2026

Let g(x) be a function such that g(a + b) = g(a). g(b) ∀ a,b ∈ R. If zero is not an element in range of g, then g(x). g(– x) is equal to

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Ans. 1

Sol. Put a = b = 0

⇒ g(0) = g 2 (0) ⇒ g(0) = 1 (as g(0) ≠ 0)

Again put a = x, b = – x

⇒ g(0) = g(x) g(–x) = 1

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