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If `f(x+1/2)+f(x-1/2)=f(x)fora l lx in R ,`then the period of `f(x)`is1 (b)2 (c) 3(d) 4A. 1B. 2C. 3D. 4 |
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Answer» Correct Answer - C `f(x+(1)/(2))+f(x-(1)/(2))=f(x) " (1)" ` Replacing x by `(x+(1)/(2)),` we get `f(x+1)+f(x)=f(x+(1)/(2)) " (2)" ` ` or f(x+1)+f(x-(1)/(2))=0 " (from (1) and (2))" ` ` or f(x+(3)/(2))= - f(x) " "("Replcing x by "(x+(1)/(2)))` ` or f(x+3) = -f(x+(3)/(2))=f(x) " " ("Replacing x by "(x+(3)/(2)))` Therefore, f(x) is periodic with period 3. |
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