Use the functions f(x)=7x3−3x2−x+14 f x = 7 x 3 - 3 x 2 - x + 14 and g(x)=2x3+2x+5 g x = 2 x 3 + 2 x + 5 as examples to show that the set of polynomials is closed under subtraction.

The given set of polynomials f(x) and g(x) are closed under subtraction.

Step-by-step explanation:

Given that the functions f ad g are defined by

and respectively.

To  show that the set of polynomials is closed under subtraction :

Now subtract the given polynomials

∴

When subtracting the polynomials the variables and their exponents remains same only variation in their coefficients.Hence the given polynomials f(x) and g(x) are closed under subtraction.

∴ are closed under subtraction,

Hence showed.