... what "more results"? "more" suggests you have already got some results. What results have you got so far?i would like to squeeze some more results from this angle and can not.
An odd function is a mathematical function where f(-x) = -f(x). In other words, when you replace x with its negative counterpart, the function outputs the negative of its original value. Graphically, this means that the function is symmetric about the origin.
An even function is a mathematical function where f(-x) = f(x). This means that when you replace x with its negative counterpart, the function outputs the same value as its original input. Graphically, this means that the function is symmetric about the y-axis.
To determine if a function is odd or even, you can use the properties mentioned in the previous questions. If f(-x) = -f(x), then the function is odd. If f(-x) = f(x), then the function is even. You can also look at the graph of the function and see if it exhibits the appropriate symmetry.
Periodicity in a function means that the function repeats itself at regular intervals. This means that after a certain value of x, the function will start to repeat its output values. This can be seen in trigonometric functions, where the sine and cosine functions have a period of 2π.
No, a function cannot be both odd and even. This is because the properties of odd and even functions are mutually exclusive. If a function is odd, it means that it is symmetric about the origin. If it is even, it means that it is symmetric about the y-axis. These two types of symmetry cannot coexist in the same function.