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

A
2
B
4
C
8
D
16

Solution

## The correct option is D 16f(2x+3)+f(2x+7)=2→(1) Replace x by x+1⇒f(2x+5)+f(2x+9)=2 Replace x by x+2→f(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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