1. **State the problem:** We are given two functions: $f(x) = 2x + 3$ and $g(x) = 3[f(x)]^2 - 2$. We need to find the explicit form of $g(x)$ in terms of $x$. 2. **Recall the formula:** The function $g(x)$ is defined in terms of $f(x)$ as: $$g(x) = 3[f(x)]^2 - 2$$ This means we first find $f(x)$, then square it, multiply by 3, and subtract 2. 3. **Substitute $f(x)$ into $g(x)$:** $$g(x) = 3(2x + 3)^2 - 2$$ 4. **Expand the square:** $$(2x + 3)^2 = (2x)^2 + 2 \times 2x \times 3 + 3^2 = 4x^2 + 12x + 9$$ 5. **Multiply by 3:** $$3(4x^2 + 12x + 9) = 12x^2 + 36x + 27$$ 6. **Subtract 2:** $$g(x) = 12x^2 + 36x + 27 - 2 = 12x^2 + 36x + 25$$ 7. **Final answer:** $$\boxed{g(x) = 12x^2 + 36x + 25}$$ This is the explicit form of $g(x)$ in terms of $x$.