Creating an odd function $f(x)$ such that $g(x) = f(x - 18)$ is an even function

Question

I am tasked with finding an example of a function $f(x)$ such that the function $g(x) = f(x-18)$ is an even function.

I understand even and odd functions. However, I am unsure how to create an odd function such that shifting it will make it even. All help is appreciated.

Answer 1

Let $f(x)=(x+18)^2$. Then, $g(x)=f(x-18)=x^2$, which is clearly an even function.

In general, $f(x)=(x+18)^n \ \forall $ even $n$ works too.