Question

For functions f(x)=2x^2−4x+3 and g(x)=x^2−2x−6, find a. (f+g)(x) b. (f+g)(3).

Answer 1

a) 3x^2-6x-3

b) 6

Explanation:

f(x)=2x^2−4x+3

g(x)=x^2−2x−6

a) (f+g)(x) = (2x^2−4x+3) + (x^2−2x−6)

collect like terms

(f+g)(x) = 2x^2+x^2-4x-2x+3-6

(f+g)(x) = 3x^2-6x-3

b) (f+g)(3). This implies that x=3

recall (f+g)(3) = 3x^2-6x-3

(f+g)(3) = 3(3)^2-6(3)-3 = 27-18-3

(f+g)(3) = 27-21 =6