\( f(x)=\left\{\begin{array}{cc}2 x-1 ; & x<-2 \\ -x^{2}+5 ; & -2 \leq x<2 \\ -2[-x+1] ; & x \geq 2\end{array}\right. \) Given: find the values for the following. Type the final answer in the blank. If the answer is No solution/does not exist, type DNE. \( f(-2)= \) \( f(4.6)= \)

To evaluate the function \( f(x) \) at the given points, we'll use the appropriate piece of the piecewise function based on the value of \( x \). The function is defined as: \[ f(x) = \begin{cases} 2x - 1 & \text{if } x < -2 \\ -x^2 + 5 & \text{if } -2 \leq x < 2 \\ -2(-x + 1) & \text{if } x \geq 2 \end{cases} \] ### 1. Evaluating \( f(-2) \): Since \( -2 \) falls in the interval \( -2 \leq x < 2 \), we use the second piece: \[ f(-2) = -(-2)^2 + 5 = -4 + 5 = 1 \] ### 2. Evaluating \( f(4.6) \): Since \( 4.6 \geq 2 \), we use the third piece: \[ f(4.6) = -2(-4.6 + 1) = -2(-3.6) = 7.2 \] **Final Answers:** - \( f(-2) = 1 \) - \( f(4.6) = 7.2 \)