Given: g (x) =

x-4 and h (x) = 2x - 8.

What are the restrictions on the domain of g h?

XT

DONE

x > = 6

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)

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