\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]

To find \( f \circ g(x) \), we need to compose the functions \( f(x) \) and \( g(x) \). This means we will substitute \( g(x) \) into \( f(x) \). First, we calculate \( g(x) \): \[ g(x) = 2x - 3 \] Now we substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) \] Next, we apply the function \( f \) to the expression \( 2x - 3 \): \[ f(x) = 3x + 4 \quad \text{hence} \quad f(2x - 3) = 3(2x - 3) + 4 \] Now, let's simplify: \[ = 6x - 9 + 4 \] \[ = 6x - 5 \] So the final result for \( f \circ g(x) \) is: \[ f \circ g(x) = 6x - 5 \]