Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If f(x) is a function defined ∀ x ∈ R and f(x) + f(–x) = 0 ∀ x ∈ 
and has period T, then prove that φ (x) = 
is also periodic with period T.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
φ (x) = 
φ (x + T) = 
= 
+ 
= φ (x) + 
= φ (x) + 
= φ (x) + 
(by using shifting property)
= φ (x) + 
= φ (x) + 
= φ (x) + 0 = φ (x) 
∴ φ (x + T) = φ (x)
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