ehild said:Just try to substitute some value for x, say x=2 and x=-2. If f(2) is not equal either to f(-2) or -f(-2) than the function is neither odd nor even.
ehild
An even function is a mathematical function in which for any input value x, the output value f(x) is equal to the output value when x is replaced by -x.
A function is even if it is symmetric about the y-axis, meaning that when reflected across the y-axis, the graph of the function remains unchanged. A function is odd if it is symmetric about the origin, meaning that when reflected across the origin, the graph of the function remains unchanged.
The main difference between an even and an odd function is their symmetry. Even functions are symmetric about the y-axis, while odd functions are symmetric about the origin. Additionally, even functions have only even powers of x, while odd functions have only odd powers of x.
No, a function cannot be both even and odd. This is because even and odd functions have different symmetry properties that cannot be satisfied simultaneously.
If a function does not exhibit symmetry about the y-axis or the origin, then it is neither even nor odd. In other words, if the function is not symmetric when reflected across the y-axis or the origin, it is neither even nor odd.