Answer:
[tex][0,+\infty)[/tex]
Step-by-step explanation:
A domain is the range of x values or input values that can be substituted for the x-terms in a function to produce a real value.
Restrictions are a set of x values that make a function produce an imaginary value.
[tex]\hrulefill[/tex]
The problem asks for the product's restriction, so we must identify the domains of g(x) and h(x).
The function h(x) = 2x - 8 is a linear function, thus its domain is all real numbers: [tex](-\infty,+\infty)[/tex].
The function g(x) = [tex]\sqrt x - 4[/tex] is a square root function, thus it does have a restriction.
Noticing the input value is under the radical means any x-values that make the radical undefined are a part of the restriction.
Knowing that all negative values make a radical undefined means that the domain, is [tex][0,+\infty)[/tex], this expresses that all non-negative values are suitable for g(x)'s domain.
Since there's a restriction for one of the functions, the product will have one too: [tex][0,+\infty)[/tex].
[tex]\dotfill[/tex]
This can be verified by graphing the product of g(x) and h(x), the domain of the function starts from 0 and goes in the positive infinity direction or rightwards.
