Question

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.

Answer 1

Since f is only defined on [-8,4] g(x) is only defined on [4,-2]=[-2,4]

That is, g(-2) = f(4) and if you try to evaluate g(-3) = f(6) that is not defined.

Play around a bit and you'll see that the domain of g is that of f, divided by -2.

Answer 2

I'm still a bit confused