Question

Find the following.

f(x) = x + 8, g(x) = x − 8

(a) (f + g)(x) =

(b) (f − g)(x) =

(c) (fg)(x) =

(d) (f/g)(x) =

What is the domain of f/g?
(Enter your answer using interval notation.)

Answer 1

(f + g)(x) = 2x

(f - g)(x) = 16

(fg)(x) =
`x^(2)` - 64

(f/g)(x) = (x + 8)/(x - 8) Domain: x < 8 ∪ x > 8

Explanation:

(f + g)(x) = f(x) + g(x) = x + 8 + x - 8 = 2x

(f - g)(x) = f(x) - g(x) = x + 8 - (x - 8) = x + 8 - x + 8 = 16

(fg)(x) = f(x)g(x) = (x + 8)(x - 8) =
`x^(2)` - 64

(f/g)(x) = f(x)/g(x) = (x + 8)/(x - 8)

x - 8 ≠ 0

x ≠ 8

Domain: x < 8 ∪ x > 8