Pure Maths
2010-12-19 2:06 am
Let f(x) and g(x) be two periodic functions with the periods S and T respectively. If S/T is a rational number prove that f(x)+g(x) is also a periodic function.
回答 (1)
2010-12-19 2:17 am
✔ 最佳答案
Since f(x) and g(x) are periodic function, for all integer nf(x+nS)=f(x) and g(x+nT)=g(x)Since S/T is rational, we can express S/T = a/b where a and b are integers=> bS = aT = P, sayFor all integer n, nP = nbS = naTf(x+nP) + g(x+nP) = f(x+nbS)+g(x+naT) = f(x) + g(x)Hence f(x) + g(x) is periodic
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