Question

ƒ(x)=sqrt(8x) and g(x)=1/(x − 4)
which value is in the domain of FoG

Answer 1

1. Determine what is the rule for function $(f\circ g)(x).$

$(f\circ g)(x)=f(g(x))=f\left(\dfrac{1}{x-4}\right)=\sqrt{8\cdot \dfrac{1}{x-4}}=\sqrt{\dfrac{8}{x-4}}.$

2. The domain of the function $(f\circ g)(x)$ - all x that sutisfy:

• $x-4\neq 0;$
• $\dfrac{8}{x-4}\ge 0.$

3. Solve them:

• $x\neq 4;$
• $x-4\ge 0\Rightarrow x\ge 4.$

Then you can state that $x>4$ is the domain.

Answer: x>4.