To find \( f(-5.8) \) using the function rule \( f(x) = (-6.82 - 1.4x)^2 \), we start by substituting \( -5.8 \) for \( x \):
\[ f(-5.8) = (-6.82 - 1.4 \times -5.8)^2 \]
Now, calculate \( 1.4 \times -5.8 \):
\[ 1.4 \times -5.8 = -8.12 \]
Next, substitute this value back into the function:
\[ f(-5.8) = (-6.82 - (-8.12))^2 \]
Simplify the expression inside the parentheses:
\[ -6.82 + 8.12 = 1.3 \]
Now, substitute this back into our function:
\[ f(-5.8) = (1.3)^2 \]
Finally, calculate \( (1.3)^2 \):
\[ f(-5.8) = 1.69 \]
Thus, the result is:
\[ \boxed{1.69} \]
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