24) If \( f(x)=\left\{\begin{array}{lll}-4 x+3, & x<3 \\ -x^{3} & , & 3 \leq x \leq 8, \\ 3 x^{2}+1 & , & x>8\end{array}\right. \) \( \begin{array}{llll}\text { (a) }-37 & \text { (b) }-1000 & \text { (c) } 301 & \text { (d) } 43)=\ldots \ldots \ldots \ldots\end{array} \)

To solve this problem, we need to find the value of \( f(3) \) since the function \( f(x) \) is defined differently for different intervals of \( x \). The value of \( f(3) \) will be the value of the function at \( x = 3 \). Given the function: \[ f(x)=\left\{\begin{array}{lll} -4x+3, & x<3 \\ -x^3, & 3 \leq x \leq 8 \\ 3x^2+1, & x>8 \end{array}\right. \] We need to use the second piece of the function definition since \( x = 3 \) falls within the interval \( 3 \leq x \leq 8 \). So, we calculate \( f(3) \) using the second piece of the function: \[ f(3) = -3^3 \] Now, let's calculate the value: \[ f(3) = -(3 \times 3 \times 3) \] \[ f(3) = -27 \] Therefore, the value of \( f(3) \) is \( -27 \). However, this value does not match any of the options provided in the problem. It's possible that there might be a mistake in the options or in the problem statement itself. If we are to choose from the given options, none of them are correct based on the calculation.