\(\text{Suppose a function $f(x)$ is defined on the domain $[-8,4]$. If we define a new function $g(x)$ by $$g(x) = f(-2x),$$ then what is the domain of $g(x)$? Express your answer in interval notation.}\)

If f(x) is defined on [ -8, 4].....this implies that the function is defined for f(-8) to f(4) inclusive

So

g(x) = f(-2x) = f(-8) implies that -2x = - 8 ⇒ x = 4

And

g(x) = f(-2x) = f(4) implies that -2x = 4 ⇒ x = -2

So....the domain for g is [ -2, 4 ]