given: $g(x)=sqrt{x - 4}$ and $h(x)=2x - 8$. what are the restrictions on the domain of $gcirc h$…
given: $g(x)=sqrt{x - 4}$ and $h(x)=2x - 8$. what are the restrictions on the domain of $gcirc h$? $xgeqsquare$ done
Answer
Explanation:
Step1: Find the composition $g\circ h$
$(g\circ h)(x)=g(h(x))=\sqrt{(2x - 8)-4}=\sqrt{2x-12}$
Step2: Determine the domain - set the radicand non - negative
For $\sqrt{2x - 12}$ to be a real number, $2x-12\geq0$. Solve the inequality: $2x-12\geq0$ $2x\geq12$ $x\geq6$
Answer:
$6$