Consider the piecewise function \( f(x) \) defined as follows:
\[ 
f(x) = 
\begin{cases} 
x^2 - 4x + 3 & \text{if } x \leq 2 \\
2x^2 - 8x + 6 & \text{if } x > 2
\end{cases}
\]
Find the value of \( f(x) \) at \( x = 1 \) and \( x = 3 \). Let's think step by step and output the final answer within \boxed{}.
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