You answered that f(x) is not even because [tex]\lfloor{f(x)}\rfloor \ne f(x)[/tex].

It's true that f(x) is not even, but I don't think your reason why is valid.

f(x) is not even because sin(x) is not even.

Consider the following function g.

g(x) = 3.5 + b*cos(x)

This is an even function because cos(x) is an even function.

If we let b = 1, for an example, here's the graph of [tex]g(x)[/tex] and [tex]\lfloor{g(x)}\rfloor[/tex].

[tex]\lfloor{g(x)}\rfloor \ne g(x)[/tex], yet g(x) is even.

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