For this case we have the following functions:
[tex]f (x) = 4x\\g (x) = x + 6[/tex]
By definition of composition of functions we have to:
[tex](f_ {o} g) (x) = f (g (x))[/tex]
So:
[tex]f (g (x)) = 4 (x + 6) = 4x + 24[/tex]
By definition, the domain of a function is given by all the values for which the function is defined. The compound function[tex](f_ {o} g) (x)[/tex]is defined for all real numbers.
ANswer:
The domain of [tex](f_ {o} g) (x)[/tex] is given by all real numbers.
Domain ∈ (-∞,∞)
