Question

What is the answer to this question?

Answer 1

Answer:

Restriction on the domain is x ≥ 6.

Step-by-step 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: $x\geq6$

Step-by-step explanation:

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

$g\°h=\sqrt{(2x-8)-4}$

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

$g\°h=\sqrt{2x-12}$

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 $x\geq6$