Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Let f be a real valued function defined for all real numbers x such that for some fixed
a > 0, f(x + a) = 
+ 
∀ x.
Show that the function is periodic with period 2a.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Sol. f(x + a) = 
+ 
⇒ f(x + 2a) = 
+ 
⇒ f(x + 2a) = 
+ 
⇒ f(x + 2a) = 
+
⇒ f(x + 2a) = 
+ 
⇒ f(x + 2a) = 
+ 
⇒ f (x + 2a) = 
+ 
⇒ f(x + 2a) = 
+ 
⇒ f(x + 2a) = f(x) … 
Thus f(x) is period and the period is 2a.
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