For this case we have the following equations:
[tex]f (x) = \sqrt {6x}\\g (x) = x-3[/tex]
We must find [tex](f_ {o} g) (x):[/tex]
By definition of composition of functions we have to:
[tex](f_ {o} g) (x) = f (g (x))[/tex]
So:
[tex](f_ {o} g) (x) = \sqrt {6 (x-3)}[/tex]
We must find the domain of f (g (x)). The domain will be given by the values for which the function is defined. That is to say:
[tex]6 (x-3) \geq0\\(x-3) \geq0\\x \geq3[/tex]
Then, the domain is given by [3, ∞)
Answer:
The smallest number that is the domain of the composite function is 3
