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Question

If f: R  R is a function satisfying the functional relation f(2x+3)+f(2x+7)=2,xϵR then period of f(x) is


Your Answer
A
2
Your Answer
B
4
Your Answer
C
8
Correct Answer
D
16

Solution

The correct option is D 16
f(2x+3)+f(2x+7)=2(1)
Replace x by x+1f(2x+5)+f(2x+9)=2
Replace x by x+2f(2x+7)+f(2x+11)=2(2)
(1)(2)f(2x+3)=f(2x+11)
period of f(2x) is 8, hence period of f(x) will be 16
period = 16

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