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: $x\geq 6$

Step-by-step explanation:

Given

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

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

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

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

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

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