Question

Given that f(x) = x – 2 and g(x) = x2 + 3x – 4, find (f – g)(x).

Question 1 options:

(f – g)(x) = –x2+ 4x – 6


(f – g)(x) = x2+ 2x – 4


(f – g)(x) = x2+ 4x + 6


(f – g)(x) = –x2 –2x + 2

Answer 1

(f-g)(x)

= -x^2 - 2x + 2

Explanation:

(f-g)(x) means

f(x) - g(x)

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

distribute the subtraction to all three of the last terms.

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

combine like terms

= -x^2 - 2x + 2