\( \left. \begin{array} { l } { f ( x ) = ( - x ) ^ { 3 } - x \cdot - x + 11 } \\ { a \cdot f ( 3 ) } \\ { b \cdot f ( - 3 ) } \end{array} \right. \)

Let’s dive into the function \( f(x) = (-x)^3 - x \cdot -x + 11 \). If we first simplify it, we see that \( (-x)^3 = -x^3 \) and \( -x \cdot -x = x^2 \). So \( f(x) \) becomes \( f(x) = -x^3 + x^2 + 11 \). Now, to find \( f(3) \): \[ f(3) = -3^3 + 3^2 + 11 = -27 + 9 + 11 = -7. \] Next, for \( f(-3) \): \[ f(-3) = -(-3)^3 + (-3)^2 + 11 = 27 + 9 + 11 = 47. \] So \( a \cdot f(3) = a \cdot (-7) \) and \( b \cdot f(-3) = b \cdot 47 \). You can play with values of \( a \) and \( b \) to get interesting results!