Question

Given f(x) = 2x-1 and g(x) = x^2+7 , find the following.

(f+g)(x)


(f-g)(x)



(f x g)(x)


( f/G) (x)


f[g(-8)]



g[f(1)]

Answer 1

(f+g)(x) = 2x - 1 + x^2 + 7 = x^2 + 2x + 6

(f-g)(x) = 2x - 1 - x^2 - 7 = -x^2 + 2x - 8

(f*g)(x) = (2x - 1)(x^2 - 7) = 2x^3 - 14x - x^2 + 7 = 2x^3 - x^2 - 14x + 7

(f/g)(x) = (2x - 1)/(x^2 - 7) - No simplification

f(g(-8)) = 2((-8)^2) - 7) - 1
            = 2(64 - 7) -1
            = 2(57) - 1 = 114 - 1 = 113

g(f(1))  = (2(1) - 1)^2 - 7
            = (2 - 1)^2 - 7
            = 1^2 - 7 = 1 - 7 = -6