Given: $$ g(x)=\sqrt{x-4} $$ and $$ h(x)=2 x-8 $$. What are the restrictions on the domain of $$ g \circ h $$ ? $$ x \geq \square $$ DONE:

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1. The composition $$ g \circ h $$ means we need to consider $$ g(h(x)) $$.
2. Since $$ g(x) = \sqrt{x-4} $$, the radicand must be nonnegative. This gives the restriction:
   $$
   h(x)-4 \geq 0
   $$
3. Substitute $$ h(x) = 2x-8 $$ into the inequality:
   $$
   2x-8-4 \geq 0
   $$
4. Simplify the inequality:
   $$
   2x - 12 \geq 0
   $$
5. Solve for $$ x $$:
   $$
   2x \geq 12 \quad \Rightarrow \quad x \geq 6
   $$
   
Thus, the domain restriction for $$ g \circ h $$ is $$ x \geq 6 $$.
The domain restriction for $$ g \circ h $$ is $$ x \geq 6 $$.

Given: and .
What are the restrictions on the domain of ?

DONE:

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