Q.

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

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a

2

b

4

c

8

d

12

answer is B.

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Detailed 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 getf (2x + 3) – f (2x + 11) = 0i.e., f (2x + 3) = f (2x + 11) ⇒ T = 4
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Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation
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