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Is there a function that is both even and odd?
Yes f(x)=0 is both even and odd
Can a function be both even and odd functions?
yes
Is fx equals c an even or odd function?
Even (unless c = 0 in which case it is either or both!)
How a function is even and odd?
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).
Is the sine functions an odd function?
Yes. Along with the tangent function, sine is an odd function. Cosine, however, is an even function.
