Question

Help please, here is the direct question

Answer 1

(a)
`$ (4)/(9) $`

(b) -6, 2

Explanation:

Given: g(x) = x + 1

h(x) = (x + 6)(x - 2)

Therefore,
`$ (g(x))/(h(x)) = (x + 1)/((x + 6)(x - 2)) $`

(a)
`$ (g)/(h)(3) = (3 + 1)/((3 + 6)(3 - 2)) $`

`$ \implies (g)/(h)(3) = (4)/(9 . 1) = (4)/(9) $`

Therefore, g/h(3) = 4/9

(b) Values not in domain means we have to determine for which values of x the function becomes undefined.

This happens when the denominator becomes zero.

That means h(x) = 0

⇒ (x + 6)(x - 2) = 0

⇒ x = -6 or x = 2

Therefore, when x takes one or both of these values we can say that the function
`$ (g)/(h) $` becomes undefined.