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

Simplify the expression by following steps: - step0: Multiply the terms: \(f\left(gx\right)\) - step1: Multiply the terms: \(fgx\) Substitute \( x=2x-3 \) into the expression \( 3(2x - 3) + 4 \). Evaluate the expression by following steps: - step0: Evaluate: \(3\left(2x-3\right)+4\) - step1: Substitute: \(3\left(2\left(2x-3\right)-3\right)+4\) - step2: Subtract the terms: \(3\left(4x-9\right)+4\) - step3: Expand the expression: \(12x-27+4\) - step4: Add the numbers: \(12x-23\) To find \( f \circ g(x) \), we need to substitute \( g(x) \) into \( f(x) \). 1. **Identify the functions:** - \( f(x) = 3x + 4 \) - \( g(x) = 2x - 3 \) 2. **Substitute \( g(x) \) into \( f(x) \):** \[ f(g(x)) = f(2x - 3) \] 3. **Replace \( x \) in \( f(x) \) with \( g(x) \):** \[ f(g(x)) = 3(2x - 3) + 4 \] 4. **Distribute and simplify:** \[ = 6x - 9 + 4 \] \[ = 6x - 5 \] Thus, the result of \( f \circ g(x) \) is: \[ f \circ g(x) = 6x - 5 \]