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

Simplify the expression by following steps: - step0: Multiply the terms: \(f\left(gx\right)\) - step1: Multiply the terms: \(fgx\) Expand the expression \( 3(2x - 3) + 4 \) Simplify the expression by following steps: - step0: Add the terms: \(3\left(2x-3\right)+4\) - step1: Expand the expression: \(6x-9+4\) - step2: Add the numbers: \(6x-5\) To find \( f \circ g(x) \), we need to substitute \( g(x) \) into \( f(x) \). 1. We have the functions: \[ f(x) = 3x + 4 \] \[ g(x) = 2x - 3 \] 2. Now, we substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(2x - 3) \] 3. Substitute \( 2x - 3 \) into \( f(x) \): \[ f(2x - 3) = 3(2x - 3) + 4 \] 4. Now, we expand this expression: \[ = 6x - 9 + 4 \] \[ = 6x - 5 \] Thus, the result of \( f \circ g(x) \) is: \[ f \circ g(x) = 6x - 5 \]