A problem about the period of function If f (x) is an odd function on R and an increasing function on (- 1,0), and f (x + 2) = - f (x), find the period of F (x)? The answer is f (x) = - f (x + 2) = f (x + 2 + 2) = f (x + 4). Why can't f (x) = - f (x + 2) be used directly, and the period is 2 | Math enthusiast | Mathematical art

A problem about the period of function If f (x) is an odd function on R and an increasing function on (- 1,0), and f (x + 2) = - f (x), find the period of F (x)? The answer is f (x) = - f (x + 2) = f (x + 2 + 2) = f (x + 4). Why can't f (x) = - f (x + 2) be used directly, and the period is 2

The definition of periodic function is that f (x) = f (x + T) holds in the whole domain, then f (x) takes t as the period
So we have to construct such a form to get the period~
But f (x) = - f (x + 2) can't find the period directly~

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