\( 1 \leftarrow \) If \( f(x)=\left\{\begin{array}{cc}3 x-2 & \text { if }-3 \leq x \leq 4 \\ x^{3}-4 & \text { if } 4

Ask by Fitzgerald Chang. in the United States

Mar 19,2025

To find \( f(0) \), we need to look at the function \( f(x) \) defined piecewise. Since \( 0 \) falls within the range of the first piece \( -3 \leq x \leq 4 \), we will use that equation: \[ f(0) = 3(0) - 2 = -2. \] Next, let's find the values for parts (b), (c), and (d). (b) \( f(1) \): Since \( 1 \) also falls within the first piece, we continue with: \[ f(1) = 3(1) - 2 = 3 - 2 = 1. \] (c) \( f(4) \): For \( f(4) \), we note that \( 4 \) is at the boundary condition of the first piece, thus: \[ f(4) = 3(4) - 2 = 12 - 2 = 10. \] (d) \( f(6) \): Now for \( 6 \), which falls into the second piece (since \( 4 < 6 \leq 6 \)): \[ f(6) = 6^3 - 4 = 216 - 4 = 212. \] So, the complete answers are: (a) \( f(0)=-2 \) (b) \( f(1)=1 \) (c) \( f(4)=10 \) (d) \( f(6)=212 \)