Answer:
<h3>The given set of polynomials f(x) and g(x) are closed under subtraction.</h3>
Step-by-step explanation:
Given that the functions f ad g are defined by
and respectively.
<h3>To show that the set of polynomials is closed under subtraction :</h3>
Now subtract the given polynomials
∴
- When subtracting the polynomials the variables and their exponents remains same only variation in their coefficients.
<h3>Hence the given polynomials f(x) and g(x) are closed under subtraction.</h3>
∴ are closed under subtraction,
Hence showed.