# Let <mtext>&#xA0;</mtext> f <mtext>&#xA0;</mtext> be any function which is defined for a

Let be any function which is defined for all numbers. Show that is even.

But how it can be proven that the claim holds?

And needless to say, can I completely assume "for all numbers" in the problem statements belong to a set of complex numbers(handling imaginary numbers is also required in this problem)?
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SweallySnicles3
I do not think you define the concept of "even" or "odd" functions for functions of a complex variable. I will assume it is real. You have
$g\left(-x\right)=f\left(-x\right)+f\left(-\left(-x\right)\right)=f\left(-x\right)+f\left(x\right)=g\left(x\right)$
so $g$ is even.