\( 1 \leftarrow \quad \) Let \( g \) be the function from \( S=\{0,1,2,3,4\} \) to the whole numbers \( W \) given by the formula \( g(x)=7-2 x+x^{2} \). (a) Find \( g(0), g(1), g(2), g(3) \), and \( g(4) \). (b) What is the range of \( g \) ? (a) \( g(0)=7, g(1)=\square \)

Let's start by calculating the values of \( g(x) \) for each \( x \) in \( S = \{0, 1, 2, 3, 4\} \). - For \( g(0) \): \[ g(0) = 7 - 2(0) + (0)^2 = 7 - 0 + 0 = 7 \] - For \( g(1) \): \[ g(1) = 7 - 2(1) + (1)^2 = 7 - 2 + 1 = 6 \] - For \( g(2) \): \[ g(2) = 7 - 2(2) + (2)^2 = 7 - 4 + 4 = 7 \] - For \( g(3) \): \[ g(3) = 7 - 2(3) + (3)^2 = 7 - 6 + 9 = 10 \] - For \( g(4) \): \[ g(4) = 7 - 2(4) + (4)^2 = 7 - 8 + 16 = 15 \] So, \( g(0) = 7, g(1) = 6, g(2) = 7, g(3) = 10, g(4) = 15 \). Now, let's summarize: - \( g(0) = 7 \) - \( g(1) = 6 \) - \( g(2) = 7 \) - \( g(3) = 10 \) - \( g(4) = 15 \) Now, for part (b), the range of \( g \) involves finding all unique values obtained: - The values are \( 6, 7, 10, 15 \). - Therefore, the range of \( g \) is \(\{6, 7, 10, 15\}\) which includes 6 (from \( g(1) \)), 7 (from \( g(0) \) and \( g(2) \)), 10 (from \( g(3) \)), and 15 (from \( g(4) \)). In conclusion, \( g(1) = 6 \) and the range of \( g \) is \(\{6, 7, 10, 15\}\).