Finding (f-g)(x) and (f-g)(5)

Question

f(x) = x² - 6x and g(x) = 1 - x

Find (f - g)(x) and (f - g)(5).

Answer 1

(f-g)(x) is stating to subtract g(x) from f(x). Therefor, (f-g)(x) = (x²-6x) - (1-x) = x²-6x+x-1 = x²-5x-1

(f-g)(5) is stating to do the above process with 5 substituted for x. You can substitute 5 for x before or after you combine the functions.

Before: f(5)=5²-6(5)= -5 g(5) = 1-5 = -4

(f-g)(5) = f(5)-g(5) = -5 - (-4) = -1

After : (f-g)(x) = x²-5x-1 substitute 5 for x (f-g)(5) = 5²-5(5)-1 = -1