Question

Find (f-g)(x) for the following functions. f(x) = 12x + 20 g(x) = –11x2 + 10x + 33

11x2 + 2x – 13

–11x2 – 2x + 13

23x2 – 10x – 13

–11x2 – 2x – 13

Answer 1

11x2 + 2x - 13

Explanation:

Let's notice that (f-g)(x) is equal to f(x)-g(x) because f(x) and g(x) are polynomial functions. Therefore, we just have to do a sum of polynomials.

Let's remember that, when adding or subtracting polynomials, we have to add or subtract the coefficients of like terms (this means, the ones that have the same exponent for the x) .

(f-g)(x) = f(x)-g(x) = 12x + 20 - (–11x2 + 10x + 33)

Don't forget to put the g(x) between parenthesis because the minus sign affects all the terms and changes their signs.

12x + 20 + 11x2 - 10x - 33 =

11x2 + (12x - 10x) + (20 - 33) =

11x2 + 2x - 13

Answer 2

11x2 + 2x-13

Explanation:

We must build the new function f-g, which turns to be a sum between polynomials.

f(x)-g(x)= 12x+20 + 11x2- 10x-33

f(x)-g(x)= 12x+20 + 11x2- 10x-33

f(x)-g(x)= 11x2 + 2x-13