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 $f(x-2)$.
 A: 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:
$$\color{green}{\boxed{f(x-2)=(x-2)^2-3(x-2)+1}}$$
A: Hint: You have $f(x)=x^2-3x+1$, now instead of $x$ just put $x-2$ and evaluate: $$f(x-2)=(x-2)^2-3(x-2)+1.$$
In general, if you have $f(x)$ and you want to find $f(m)$ just replace all the $x$ with $m$. 
A: Wherever you see $x$, replace it by $x - 2$:
$f(x - 2) = (x-2)^{2} - 3(x-2) + 1$
A: The eaisest way to think and do these kinds of problems is to simply just say that x = x-2, and directly substitute directly into the original function. 
$$f(x) = x^2 - 3x + 1$$ 
Let $x = x - 2$
Sub back into original function for $x$
   \begin{eqnarray*}    
   f(x-2) &=& (x-2)^2-3(x-2)+1\\
          &=& x^2 -4x + 4 -3x + 6 + 1\\
          &=& x^2 -7x + 11
\end{eqnarray*}
