Question

2a. Determine (𝑓 x 𝑔)(𝑥) in simplified form and state its domain, given 𝑓(𝑥) = 𝑙𝑜𝑔𝑥 and 𝑔(𝑥) =2 /𝑥−6

2b. Determine (𝑓 ÷ 𝑔)(𝑥) in simplified form and state its domain, given 𝑓(𝑥) = 𝑥 + 8 and 𝑔(𝑥) = √𝑥 − 8 (square root is over the whole expression "x-8"

2c. Determine (𝑓𝑜𝑔)(𝑥) in simplified form and state its domain, given 𝑓(𝑥) =
3/𝑥−2 and 𝑔(𝑥) =𝑥/2𝑥−3

Answer 1

Why do f (x) and g (x) add up in question 2b? shouldn't they be divided?

Answer 2

(f*g)(x) = f(x)*g(x) = logx * (2/(x-6))

(f+g)(x) = f(x)+g(x) = .....
(f•g)(x) = f(g(x)) = 3/(g(x)-2) = 3/((x/(2x-3))-3) = (9-6x)/(5x-9)