Question

Let f(x) = 8x and g(x) = x - 3. What's
the smallest number that is in the domain of
fog?

Answer 1

The smallest number that is in the domain of fog is 3

Explanation:

f(x) =
`√(8x)` (as corrected in comments)

g(x) = x-3

we need to find fog = f(g(x))

For finding f(g(x)) we put the value of g(x) inside the f(x)

f(g(x))=
`√(8(x-3))`

The domain of this function is x ≥ 3

because if value of x is less than 3 than the result would be negative and we know √f(x) ≥ 0

So, the smallest number that is in the domain of fog is 3