Question

Given: g(x) = Square Root x - 4 and h(x) = 2x-8 What are the restrictions on the domain of g ⋅ h? x ≥ ____

Answer 1

Answer:
`x\geq 6`

Explanation:

Given

`g(x)=√(x-4)\\h(x)=2x-8`

Now, g of h i.e.
`g(h(x))`

Put h(x) in place of x in g(x)

`\Rightarrow g(h(x))=√((2x-8)-4)\\\\\Rightarrow g(h(x))=√(2x-12)`

Now, the value inside square root must be greater than zero

`\Rightarrow 2x-12\geq 0\\\\\Rightarrow 2x\geq 12\\\\\Rightarrow x\geq 6`