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( «׸ »)
: ,

  , . , . : f(x) = xn , n , , n .

f(x) = x  .
f(x) = x^2  .
f(x) = x^3,
f(x) = x^3+1 , .

:


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X \subset \mathbb{R}, , .

  • f ,
f(-x) = f(x),\quad \forall x \in X.
  • f:X \to \mathbb{R} ,
f(-x)=-f(x), \quad \forall x \in X.

( ).

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  • O.
  • Oy.
  • f:[-X,X] \subset \mathbb{R} \to \mathbb{R} :
f(x) = g(x) + h(x),

g(x) = \frac{f(x) - f(-x)}{2},\; h(x) = \frac{f(x)+f(-x)}{2}.
  • f(x) \equiv 0  , .
  • , ,   .
  • , , ,   .
  • .
  • .
  • .
  • / .
  • ( !).
  • ,   .
    • , .
  • , .

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  • f(x) = x^{2k+1},\quad x\in \mathbb{R} k\in \mathbb{Z}  .
  • f(x) = \sin x,\quad x \in \mathbb{R}.
  • f(x) = \operatorname{tg} x,\quad x \in (-\frac{\pi}{2}; \frac{\pi}{2}).

[] ׸

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