Question

Given that ƒ(x) = 3x – 1 and g(x) = 4x2 – 5x 7, find (ƒ – g)(x). options: a) (ƒ – g)(x) = –4x2 – 2x 6 b) (ƒ – g)(x) = –4x2 2x – 6 c) (ƒ – g)(x) = –4x2 8x – 8 d) (ƒ – g)(x) = –4x2 – 8x 8

Answer 1

The result of the function (ƒ – g)(x) given that ƒ(x) = 3x – 1 and g(x) = 4x2 – 5x + 7 is (ƒ – g)(x) = -4x2 + 8x - 8.

Step-by-step explanation:

This question is dealing with the operations on functions, specifically subtraction of functions. We are asked to find (ƒ – g)(x) which means subtracting g(x) from ƒ(x).

Given the functions ƒ(x) = 3x – 1 and g(x) = 4x2 – 5x + 7, to find (ƒ – g)(x), we subtract g(x) from f(x), like so: (ƒ – g)(x) = f(x) - g(x).

In this case:

(ƒ – g)(x) = (3x – 1) - (4x2 – 5x + 7)

Be careful with signs here. This equals:

(ƒ – g)(x) = -4x2 + 8x - 8

So, the correct answer is (ƒ – g)(x) = -4x2 + 8x - 8, which corresponds to option c).

Learn more about Subtraction of Functions