Answer:
(c) x ≠ -2/3
Explanation:
You want to know the domain restrictions on (g∘h)(x), given g(x) = 1/(x+2) and h(x) = 3x.
Composition
The function h(x) is defined for all x.
The composite function (g∘h)(x) is ...
(g∘h)(x) = g(h(x)) = 1/(3x +2)
This function is undefined where the denominator is zero:
3x +2 = 0 ⇒ x = -2/3
The domain must exclude values of x where the function is undefined.
The restriction on the domain of (g∘h)(x) is x ≠ -2/3, choice C.
__
Additional comment
The function g(x) is written as (1/x) +2. If that is the intended definition of g(x), then the only domain restriction is x ≠ 0, choice A.
<95141404393>