If $ f(x)=x^2-3x+1$ then $ f(x-2) = ?$ If $ f(x)=x^2-3x+1$ then $ f(x-2) = ?$
I'm not sure how to properly deal with this function and solve for $f(x-2)$.

Of course, the simple answer would be to just write $(x-2)$ for every $x$ you see. The answer would be:
$$f(x-2)=(x-2)^2-3(x-2)+1$$
$$f(x-2)=x^2-4x+4-(3x-6)+1$$
$$f(x-2)=x^2-4x+4-3x+6+1$$
$$\color{green}{\boxed{f(x-2)=x^2-7x+11}}$$
However, I find it helpful to know why we can substitute $(x-2)$ for $x$.
What exactly are functions? I like to think of a function like a machine. This machine takes an input, processes it, and gives you an output. In the function $f(x)=x-3$, $f$ is the name of the machine, and $x$ is the input. $f$ is telling you, "If you input any $x$ into me, I will give you $x-3$ as an output!"
Let's say we want to find the value of $f(5)$. We are actually giving the machine an input of $5$. In this case, our $x$ is equal to $5$. So the output, $x-3$ is equal to $5-3=2$. This is written as $f(5)=2$.
Let's go back to the original problem, this time thinking about it with our machine analogy.
$$f(x)=x^2-3x+1$$
This function tells us that for any input $x$, the output will be $x^2-3x+1$. Now what if we input $x-2$ into the machine? Our output would be $(x-2)^2-3(x-2)+1$. Every $x$ in the  function corresponds to the input value. Therefore we can write our function like this:
$$f(\text{input})=(\text{input})^2-3(\text{input})+1$$
Our input is $x-2$, therefore:
$$\color{green}{\boxed{f(x-2)=(x-2)^2-3(x-2)+1}}$$
