1. The problem asks whether the set of polynomials $f(x)$ and $g(x)$ is closed under subtraction. 2. Recall that a set is closed under an operation if performing that operation on members of the set results in a member still in the set. 3. Here, $f(x) = a_0 + a_1x + a_2x^2 + \dots + a_nx^n$ and $g(x) = b_0 + b_1x + b_2x^2 + \dots + b_mx^m$ are polynomials. 4. Subtracting $g(x)$ from $f(x)$ gives: $$f(x) - g(x) = (a_0 - b_0) + (a_1 - b_1)x + (a_2 - b_2)x^2 + \dots + (a_k - b_k)x^k$$ where $k = \max(n,m)$, and coefficients for missing powers are treated as zero. 5. Since the subtraction of coefficients results in new coefficients, the result is still a polynomial. 6. Therefore, the set of polynomials is closed under subtraction. **Final answer:** $f(x)$ and $g(x)$ are closed under subtraction because when subtracted, the result will be a polynomial.