Answer:
(a) [tex]$ \frac{4}{9} $[/tex]
(b) -6, 2
Step-by-step explanation:
Given: g(x) = x + 1
h(x) = (x + 6)(x - 2)
Therefore, [tex]$ \frac{g(x)}{h(x)} = \frac{x + 1}{(x + 6)(x - 2)} $[/tex]
(a) [tex]$ \frac{g}{h}(3) = \frac{3 + 1}{(3 + 6)(3 - 2)} $[/tex]
[tex]$ \implies \frac{g}{h}(3) = \frac{4}{9 . 1} = \frac{4}{9} $[/tex]
Therefore, g/h(3) = 4/9
(b) Values not in domain means we have to determine for which values of x the function becomes undefined.
This happens when the denominator becomes zero.
That means h(x) = 0
⇒ (x + 6)(x - 2) = 0
⇒ x = -6 or x = 2
Therefore, when x takes one or both of these values we can say that the function [tex]$ \frac{g}{h} $[/tex] becomes undefined.
