Question

Determine the domain for each function in interval notation
(The first one pls)

Answer 1

Explanation:

f + g = x^2 + 2x + 6 - x^2

= 2x + 6

Domain is (-∝ , ∝ )

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

= 2x^2 + 2x - 6

Domain is (-∝ , ∝ )

fg = (x^2 + 2x)( 6 - x^2)

= 6x^2 - x^4 + 12x - 2x^3

Domain is (-∝ , ∝ )

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

Here x = √6 or -√6 are not included in the domain as the denominator will be zero and the function is undefined at the values.

Domain = (-∝, -√6) U (√6, ∝ )