If `f:RrarrR` is a function satisfying the property `f(x+1)+f(x+3)=2" – InterviewSolution

InterviewSolution

1.	If `f:RrarrR` is a function satisfying the property `f(x+1)+f(x+3)=2" for all" x in R` than `f` isA. periodic with period 3B. periodic with period 4C. non periodicD. periodic with period 5
Answer» Correct Answer - 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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