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I have been given an optional challenge problem at the end of one of my earlier tutorials that I am unsure how to solve. It is a question with three parts, but I would like to tackle them separately with a little help on part a.
a function $f$ is even if $f(-x) = f(x)$ for all $x$, and odd if $f(-x) = -f(x)$ for all $x$.
Now I am told to show that every polynomial is the sum of both an even and an odd function, but have no idea how to go about this.
Is the key to this question that $f(-x) = x^2$ will always $= f(x)$ $\therefore$ $x^2$ is even? I understand that, and if a secondary function was $g(-x) = x$, where x is only positive, then it would make sense that this is a odd function, but it is for all x, and therefore a negative x value in g(-x) would become positive and it wouldn't be an odd or an even function.