Question

What is (f-g)(x)

f(x)=3x+6
g(x)=-5x+2
Write your answer as a polynomial or a rational function in simplest form.

Answer 1

8x + 4

Explanation:

To find (f-g)(x), we need to subtract the function g(x) from the function f(x). Given: f(x) = 3x + 6 g(x) = -5x + 2 To subtract g(x) from f(x), we'll subtract the corresponding coefficients of x and the constant terms: (f-g)(x) = (3x + 6) - (-5x + 2) To simplify, we'll distribute the negative sign to all terms inside the parentheses: (f-g)(x) = 3x + 6 + 5x - 2 Next, we'll combine like terms by adding the coefficients of x and the constant terms: (f-g)(x) = (3x + 5x) + (6 - 2) Simplifying further: (f-g)(x) = 8x + 4 Therefore, (f-g)(x) is equal to the polynomial 8x + 4.