Question

What is the answer to this question?

Answer 1

Restriction on the domain is x ≥ 6.

Explanation:

We have given two functions.

g(x) = √x-4 and h(x) = 2x-8

We have to find the restrictions on the domain of (g o f).

(g o h)(x) = g(h(x))

(g o h)(x) = g(2x-8)

(g o h)(x) = √2x-8-4

(g o h)(x) = √2x-12

Hence, 2x-12 ≥ 0

2x ≥ 12

x ≥ 6

Hence, restriction on the domain is x ≥ 6.

Answer 2

Answer:
`x\geq6`

Explanation:

g°h indicates that you must plug the function h(x) into the function g(x) as you can see below:

`g\°h=√((2x-8)-4)`

Now you must simplify by adding like terms, as following:

`g\°h=√(2x-12)`

By definition you have that:

`2x-12\geq0`

Theen you must solve for x:

`2x\geq12\\x\geq6`

Therefore, the domain is:

{
`x` ∈R:
`x\geq6`}

Then the answer is
`x\geq6`