The function \( g \) is defined as follows. \[ g(x)=\frac{3 x+2}{7 x+12} \] Find \( g(-8) \). Simplify your answer as much as possible. If applicable, click on

To find \( g(-8) \), we will substitute \( x = -8 \) into the function \( g(x) = \frac{3x + 2}{7x + 12} \). Calculating the numerator: \[ 3(-8) + 2 = -24 + 2 = -22 \] Calculating the denominator: \[ 7(-8) + 12 = -56 + 12 = -44 \] Now substituting these values back into the function: \[ g(-8) = \frac{-22}{-44} \] Simplifying the fraction: \[ g(-8) = \frac{-22 \div -22}{-44 \div -22} = \frac{1}{2} \] Thus, \( g(-8) = \frac{1}{2} \).