A mathematical problem, periodic function If f (x) is a function defined on the set of real numbers and f (x + 2) = f (x + 1) = f (x), f (1) = Lg3 / 2, f (x) = LG15 Prove by definition that it is a periodic function
f(x+2)=f(x+1)-f(x)
f(x+3)=f(x+2)-f(x+1)=f(x+1)-f(x)-f(x+1)=-f(x)
f(x+6)=-f(x+3)=f(x)
therefore
F (x) is a function of period 6
because
f(2004)=f(6*334+0)=f(0)
because
f(2)=f(1)-f(0)
lg15=lg3/2-f(0)
f(0)=-1
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