To find \( f(1) \) using the function rule \( f(x) = 5.13 + 3.92x \), we need to substitute \( x \) with 1.
Substituting 1 into the function:
\[ f(1) = 5.13 + 3.92 \cdot 1 \]
Calculating the \( 3.92 \cdot 1 \):
\[ 3.92 \cdot 1 = 3.92 \]
Now adding this to 5.13:
\[ f(1) = 5.13 + 3.92 = 9.05 \]
Thus, the value of \( f(1) \) is:
\[ \boxed{9.05} \]