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

1. We start with the definition of a composition of functions: \[ (f \circ g)(x) = f(g(x)) \] 2. Substitute \( g(x) = 2x - 3 \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) \] 3. The function \( f(x) \) is given by \( f(x) = 3x + 4 \). Replace \( x \) with \( 2x - 3 \) in this expression: \[ f(2x - 3) = 3(2x - 3) + 4 \] 4. Distribute the 3: \[ 3(2x - 3) = 6x - 9 \] 5. Add the 4: \[ 6x - 9 + 4 = 6x - 5 \] 6. Therefore, the composition \( f \circ g(x) \) is: \[ (f \circ g)(x) = 6x - 5 \]