Question

Given:g(x)= x-4 and h(x)= 2x-8 What are the restrictions on the domain of g•h? x>

Answer 1

`g(x) =√(x-4)`

`h(x) =2x-8`

And we want to find:

`g o h(x)`

Replacing we got:

`go h(x)= √(2x-8 -4)= √(2x-12)`

And the restriction for this case would be:

`2x-12 \geq 0`

`2x \geq 12`

`x \geq 6`

Explanation:

Assumign that we have the following two functions:

`g(x) =√(x-4)`

`h(x) =2x-8`

And we want to find:

`g o h(x)`

Replacing we got:

`go h(x)= √(2x-8 -4)= √(2x-12)`

And the restriction for this case would be:

`2x-12 \geq 0`

`2x \geq 12`

`x \geq 6`