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Math Help - Interesting Question

  1. #1
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    Interesting Question

    A function f is known to have the following properties for all t: f(t+4)=f(t) and f(2+t)=f(2-t). Which of the following must be true?

    A) f is periodic with period 4
    B) f(t)>0 for all t
    C) f(0)=0
    D) f is an even function
    E) f is an odd function
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  2. #2
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    Quote Originally Posted by chaddy View Post
    A function f is known to have the following properties for all t: f(t+4)=f(t) and f(2+t)=f(2-t). Which of the following must be true?

    A) f is periodic with period 4
    B) f(t)>0 for all t
    C) f(0)=0
    D) f is an even function
    E) f is an odd function
    A) is true: f(t + 4) = f(t).

    D) is true: Let t --> t + 2 in f(2+t)=f(2-t): f(t + 4) = f(-t). But f(t + 4) = f(t). Therefore f(-t) = f(t) and so f is even.

    C) is not necessarily true. It's easy to construct examples that satisfy A) and D) but not C).
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