Question

5. If g(x) = 3x −1 and f(x) = sqrt9-x^2 then which of the following will have a domain of: [−3, 1/3) ∪ (1/3, 3]?

Answer 1

notice how the f(x) is a semicircle. remember that y^2+x^2 =r^2 is a circle with radius rlook at teh domain of g(x). The graph will look something like this. What does that tell you about the domain of that linear line?
In comparison. here's the graph of f(x)

Answer 2

i still dont understand

Answer 3

Domain is the values of x that is in the function. Notice how your line g(x) extends infinitely to the right and the left. That means that all points along the x-axis exists in that line.
Now, if you compare that to the semicircle of f(x), you'll notice that the line stops at 3 and -3 along the x-axis. That means that f(x) has a restricted domain between [-3,3]

Answer 4

okay i grt it:)