Functions (XII)
Question
If f : R → R is a function satisfying the property f (2x + 3) + f (2x + 7) = 2, ∀ x ∈ R, then the period of f (x) is
Moderate
Solution
We have,
f (2x + 3) + f (2x + 7) = 2 (1)
Replace x by x + 1,
f (2x + 5) + f (2x + 9) = 2 (2)
Now replace x by,
x + 2, f (2x + 7) + f (2x + 11) = 2 (3)
From (1) – (3), we get
f (2x + 3) – f (2x + 11) = 0
i.e., f (2x + 3) = f (2x + 11) ⇒ T = 4
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