e following: Find \( k \) so that \( g(k+3)=2 g(2 k) \) (6pts)

To determine the value of \( k \) that satisfies the equation \( g(k + 3) = 2g(2k) \), we need more information about the function \( g \). Specifically, we require a definition or properties of \( g \) to proceed with solving for \( k \). **Possible Scenarios:** 1. **If \( g \) is a Linear Function:** Suppose \( g(x) = ax + b \), where \( a \) and \( b \) are constants. \[ g(k + 3) = a(k + 3) + b = ak + 3a + b \] \[ 2g(2k) = 2(a(2k) + b) = 4ak + 2b \] Setting them equal: \[ ak + 3a + b = 4ak + 2b \] Rearranging terms: \[ -3ak + 3a - b = 0 \quad \Rightarrow \quad k = \frac{3a - b}{3a} \] This provides a formula for \( k \) in terms of \( a \) and \( b \). 2. **If \( g \) is a Non-Linear Function:** Without specific information about the form of \( g \), such as its degree or other properties, we cannot derive an explicit solution for \( k \). **Conclusion:** To find the exact value of \( k \), please provide the definition or properties of the function \( g \). Once \( g \) is specified, we can apply the appropriate methods to solve for \( k \).