Question

Let f(x) = 4x and g(x) = x + 6. What's
the smallest number that is in the domain of
fºg?

Answer 1

For this case we have the following functions:

$f (x) = 4x\\g (x) = x + 6$

By definition of composition of functions we have to:

$(f_ {o} g) (x) = f (g (x))$

So:

$f (g (x)) = 4 (x + 6) = 4x + 24$

By definition, the domain of a function is given by all the values for which the function is defined. The compound function$(f_ {o} g) (x)$is defined for all real numbers.

ANswer:

The domain of $(f_ {o} g) (x)$ is given by all real numbers.

Domain ∈ (-∞,∞)