Let f (x) be an odd function defined on R, f (x + 3) f (x) = - 1 Since a function is an odd function defined on R, why let x = 0. F (x) = 0 such that f (x + 3) f (x) = - 1 does not hold? | Math enthusiast | Mathematical art

Let f (x) be an odd function defined on R, f (x + 3) f (x) = - 1 Since a function is an odd function defined on R, why let x = 0. F (x) = 0 such that f (x + 3) f (x) = - 1 does not hold?

The domain contains x = 0
Then f (0) is meaningful
Because it's an odd function
So there must be f (0) = 0
Then when x = 0, the left side = 0
So this doesn't work

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