Question

Help please, here is the direct question

Answer 1

Answer:

(a) $\frac{4}{9}$

(b) -6, 2

Step-by-step explanation:

Given: g(x) = x + 1

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

Therefore, $\frac{g(x)}{h(x)} = \frac{x + 1}{(x + 6)(x - 2)}$

(a) $\frac{g}{h}(3) = \frac{3 + 1}{(3 + 6)(3 - 2)}$

$\implies \frac{g}{h}(3) = \frac{4}{9 . 1} = \frac{4}{9}$

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 $\frac{g}{h}$ becomes undefined.