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.
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.
I'm still a bit confused
To find the domain of the function g(x) = f(-2x), we need to consider two things:
1. The domain of the original function f(x).
2. The restrictions imposed by the transformation -2x in g(x).
Let's start with the domain of f(x), which is given as [-8,4]. This means that every x-value within the interval [-8,4] is valid for the function f(x).
Now, let's consider the transformation -2x. This transformation involves multiplying the value of x by -2. Multiplying by a negative number doesn't affect the original domain, so the domain of f(x) remains the same.
However, the transformation -2x can cause additional restrictions on the domain. In this case, since we are multiplying x by -2, the domain needs to be adjusted accordingly. To find the new domain, we divide the original domain by the absolute value of the coefficient of x in the transformation.
Dividing [-8,4] by |-2| = 2 gives us [-4,2].
Therefore, the domain of g(x) is [-4,2], expressed in interval notation.