Method of judging odd function and even function

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The definition of even function is that the domain is (-∞, +∞), about the function of Y-axis symmetry, it should be noted that the function must be on the domain when judging even function, sometimes in (-∞, +∞) the function is not odd and not even, but the scope of the domain may be even function

To judge the even function, we must first see whether the domain of the function is symmetric about the origin, and then we must substitute x into the equation f(-x)=f(x) to make the equation work

Examples of common even functions are shown below

The definition of an odd function, whose domain is (-∞, +∞), is symmetric about the origin, and f(0)=0

Odd function judgment, first of all to calculate f(0)=0, if the equation is not valid, it must not be odd function, the equation is valid, to continue to judge whether the function domain is symmetric about the origin, and then also to replace x into the equation f(-x)=-f(x), so that the equation is established

The following is an example of a common odd function

The domain must be symmetric, even function symmetric about the y axis, odd function symmetric about the origin

An odd function must satisfy f(0)=0

Odd and even functions must be continuous functions in the domain