Question

What are the restrictions on the domain of g o h?

Answer 1

Answer:

6

Step-by-step explanation:

100%

Answer 2

$g(x) = \sqrt{x-4}$ and h(x)= 2x-8

g o h is a composition function

First we find g o h

g o h is g(h(x))

We plug in h(x) in g(x)

We replace x  with 2x-8 in g(x)

$g(h(x)) = g (2x-8) = \sqrt{2x-8-4} = \sqrt{2x-12}$

$g(h(x)) = \sqrt{2x-12}$

To find domain we look at the domain of h(x) first

Domain of h(x) is set of all real numbers

now we look at the domain of g(h(x))

Negative number inside the square root is imaginary. so we ignore negative number inside the square root

So to find domain we set 2x - 12 >=0   and solve for x

2x - 12 >=0

add both sides by 12

2x >= 12

divide both sides by 2

x > = 6