InterviewSolution
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InterviewSolution
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Let `f: R to R ` be given by `f(x+(5)/(6))+f(x)=f(x+(1)/(2))+f(x+(1)/(3))` for all ` x in R ` . Then ,A. f(x) is periodicB. f(x) is evenC. `f(x+2)-f(x+1)=f(x+1)-f(x)`D. none of these |
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Answer» Correct Answer - C we have, `f(x+(5)/(6))+f(x)=f(x+(1)/(2))+f(x+(1)/(3))` for all ` x in R ` Clearly , `(x+(5)/(6))+x=(x+(1)/(2))+(x+(1)/(3))` Thus, f(x) satisfies the property f(u)+f(v)=f(a)+f(b) if u+v=a+b We observe that option (c ) satisfied this property . |
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