Question

Given functions:

f(x)=3x3+4x2−6x−7
g(x)=2x−4

Find
(f−g)(x), the subtraction of the two functions.

f−g=3x 3+4x 2−6x−7−2x+4
f−g=3x 3+4x2−8x−3
f−g=5x 2−10x−11
f−g=x3−2x 2+4x+3

Answer 1

To find (f - g)(x) for the given functions f(x) = 3x^3 + 4x^2 - 6x - 7 and g(x) = 2x - 4, we subtract g(x) from f(x), change the sign of g(x)'s terms, and combine like terms to get the result 3x^3 + 4x^2 - 8x - 3.

Step-by-step explanation:

To determine the subtraction of two functions f(x) and g(x), we simply subtract the values of g(x) from f(x) for every x. The given functions are f(x) = 3x^3 + 4x^2 - 6x - 7 and g(x) = 2x - 4. Now we need to find (f - g)(x), which can be calculated as follows:

(f - g)(x) = f(x) - g(x)

= (3x^3 + 4x^2 - 6x - 7) - (2x - 4)

When subtracting, we change the sign of the subtracted terms and then combine like terms:

= 3x^3 + 4x^2 - 6x - 7 - 2x + 4

Combine the x terms:

= 3x^3 + 4x^2 - 8x - 3

Thus, the correct subtraction of g(x) from f(x) is 3x^3 + 4x^2 - 8x - 3.