Questions: g(x)=-3x-3 for x ≠ 0 -1 for x=0 g(0)= g(7)= g(-3)=

Transcript text: 10. \(g(x)=\left\{\begin{array}{ll}-3 x-3 & \text { for } x \neq 0 \\ -1 & \text { for } x=0\end{array}\right.\) \(g(0)=\) \(g(7)=\) \(g(-3)=\)

Solution

Solution Steps

Step 1: Evaluate \( g(0) \)

The function \( g(x) \) is defined as: \[ g(x) = \begin{cases} -3x - 3 & \text{for } x \neq 0, \\ -1 & \text{for } x = 0. \end{cases} \] Since \( x = 0 \), we use the second case of the function definition: \[ g(0) = -1. \]

Step 2: Evaluate \( g(7) \)

For \( x = 7 \), which is not equal to 0, we use the first case of the function definition: \[ g(7) = -3(7) - 3 = -21 - 3 = -24. \]

Step 3: Evaluate \( g(-3) \)

For \( x = -3 \), which is not equal to 0, we again use the first case of the function definition: \[ g(-3) = -3(-3) - 3 = 9 - 3 = 6. \]