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

To find \( f \circ g(x) \), we need to substitute \( g(x) \) into \( f(x) \). First, we have: \[ g(x) = 2x - 3 \] Now, substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) \] Next, use the definition of \( f(x) \): \[ f(x) = 3x + 4 \] So, substituting \( 2x - 3 \) in place of \( x \) in \( f(x) \): \[ f(2x - 3) = 3(2x - 3) + 4 \] Now, simplify: \[ = 6x - 9 + 4 \] \[ = 6x - 5 \] Therefore, the composition \( f \circ g(x) \) is: \[ f \circ g(x) = 6x - 5 \]