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If f:RrarrR is a function satisfying the...

If `f:RrarrR` is a function satisfying the property `f(x+1)+f(x+3)=2" for all" x in R` than `f` is

A

periodic with period 3

B

periodic with period 4

C

non periodic

D

periodic with period 5

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x+1)+f(x+3)=2" (i)"`
`"Replacing x by "x+2," we get"`
`f(x+3)+f(x+5)=2" (ii)"`
Subtracting (ii) rom (i), we get
`f(x+1)=f(x+5)`
`"or "f(x)=f(x+4)`
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