Question

How do i solve this?

Answer 1

a. x+6+x-6= 2x
b. x+6-(x-6)= x+6-x+6= 12
c. (x+6)(x-6)= x^2-36
d. (x+6)/(x-6)

The interval notation of (x+6)/(x-6) or the domain is x

Answer 2

Answers: (a) 2x

(b) 12

(c) x² - 36

`\bold{(d)\ (x+6)/(x-6)}`

Domain: x ≠ 6 (-∞, 6) ∪ (6, ∞)

Explanation:

(f + g)(x) means "f(x) + g(x)"

x + 6 + x - 6 = 2x

(f - g)(x) means "f(x) - g(x)"

x + 6 - (x - 6)

x + 6 - x + 6 = 12

(fg)(x) means "f(x) × g(x)"

(x + 6) × (x - 6)

x² - 6x + 6x - 36 = x² - 36

(f/g)(x) means "f(x) ÷ g(x)"

(x + 6) ÷ (x - 6) =
`(x+6)/(x-6)`

Domain: The denominator cannot be zero, so

x - 6 ≠ 0

x ≠ 6