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The only way a function can be both even and odd is for it to ignore the input, i.e. for it to be a constant function. e.g. f(x)=4 is both even and odd.
An even function is one where f(x)=f(-x), and an odd one is where -f(x)=f(-x).
This doesn't make sense. Let's analyze.
For a function to be even, f(-x)=f(x). For a function to be odd, f(-x)=-f(x).
In this case, f(x)=4, and f(-x)=4. As such, for the first part of the even-odd definition, we have 4=4, which is true, making the function even. However, for the second part of it, we have 4=-4 (f(-x)=4, but -f(x)=-4), which is not true. Therefore constant functions are even because f(-x)=f(x), but not odd because f(-x)!=-f(x).
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Is the sine functions an odd function?
Yes. Along with the tangent function, sine is an odd function. Cosine, however, is an even function.
Is there a function that is both even and odd?
Yes f(x)=0 is both even and odd
Is f of x equal to negative x an even or odd function?
It is an odd function. Even functions use the y-axis like a mirror, and odd functions have half-circle rotational symmetry.
Can a function be both even and odd functions?
yes
Why you use even and odd function in mathematics?
If you know that a function is even (or odd), it may simplify the analysis of the function, for several purposes. One example is the calculation of definite integrals: for an odd function, the integral of a function from (-x) to (x) (note 1) is zero; for an even function, this integral is twice the integral of the function from (0) to (x). Note 1: That is, the area under the function; for negative values, this "area" is taken as negative) is
