Find the number of solution of equation (where sgn represen…

Maths Fundamental of Mathematics Greatest Integer Function, Fractional Part & Signum Function Subjective Type

Published by: CGP EDU Academic Team

Published on: August 14, 2026

Find the number of solution of equation (where sgn represent signum function)

(i) sgn (x) = |x|

(ii) sgn (x 2 – 1) = (x + 1) 2

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The correct answer is:

CHECK THE SOLUTION.

(i) 2 (ii) 2

Sol. (i) l

⇒ two solution

(ii) Case-I (x + 1) 2 = 0 & sgn (x 2 – 1) = 0 ⇒ x = – 1

Case-II (x + 1) 2 = 1 & sgn (x 2 – 1) = 1 ⇒ x = – 2

⇒ x ∈ {–1, –2}

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