Answer:
The smallest number that is in the domain is 2
Step-by-step explanation:
we have
[tex]f(x)=\sqrt{7x}[/tex]
[tex]g(x)=x-2[/tex]
we know that
[tex]fog(x)=f(g(x))[/tex]
Substitute the variable x by the function g(x) in the function f(x)
so
[tex]f(g(x))=\sqrt{7(x-2)}[/tex]
[tex]f(g(x))=\sqrt{7x-14}[/tex]
Remember that the radicand must be greater than or equal to zero
[tex]7x-14\geq 0[/tex]
Solve for x
Adds 14 both sides
[tex]7x\geq 14[/tex]
Divide by 7 both sides
[tex]x\geq 2[/tex]
The domain is the interval [2,∞)
therefore
The smallest number that is in the domain is 2
