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  • If f:R-->R is a function satisfying the property f(x+1)+f(x+3) =2 for all x belong R then period of f is

If f:R-->R is a function satisfying the property f(x+1)+f(x+3) =2 for all x belong R then period of f is

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Solution: We have,

\ f(x+1)+f(x+3)=2 .......(1)

Replacing x by x+2 , we get

\ f(x+3)+f(x+5)=2 .......(2)

From (1)-(2) we get

f(x+1)=f(x+5)\ \Rightarrow or;f(x)=f(x+4)

Hence period of f is 4

Posted by

Deependra Verma

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