Let's assume that $f(x) = x^2-4x+5$ is a function. Then, how could we find the functions $g(x), h(x)$ that are the symmetries of $f(x)$ with respect to $x, y$-axes respectively?
I came up with the following functions:
$$g(x) = -|f(x)| = -|x^2-4x+5|$$
$$h(x) = f(-|x|) = x^2+4|x|+5$$
However, I am not sure if it makes sense.
Given function $f(x)$, then $f(-x)$ represents its mirror image with respect to the $y$ axis and $-f(x)$ represents its mirror image with respect to the $x$ axis.