Suppose that f(x) is an odd function, and periodic with period 8. If f(3)=2, find f(4)+f(5), and prove that it must always have the same value.
So far I have f(3)= f(-6+8)= 2 but I don;t even know if this is right.
Finding additional function values of an odd-periodic function and period 8
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calculus
functions
1 Answers
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Since $f$ is periodic $$f(4)=f(4-8)=f(-4)\\f(5)=f(5-8)=f(-3)$$ Since $f$ is odd $$f(-4)=-f(4)\\f(-3)=-f(3)$$ Now combine these equations,I'll let you do that.