1. **State the problem:** Find the composite function $gf(x)$, which means applying $f$ first, then $g$ to the result. 2. **Recall the functions:** $$f(x) = 2x - 1$$ $$g(x) = 3x + 2$$ 3. **Write the composite function:** $$gf(x) = g(f(x)) = g(2x - 1)$$ 4. **Substitute $f(x)$ into $g$:** $$gf(x) = 3(2x - 1) + 2$$ 5. **Distribute the 3:** $$gf(x) = 3 \times 2x - 3 \times 1 + 2 = 6x - 3 + 2$$ 6. **Simplify the constants:** $$gf(x) = 6x - 1$$ **Final answer:** $$\boxed{gf(x) = 6x - 1}$$