Given figure to be the graph of the functionf(x) with three points labeled and two sets of blank axis. The domain and range off(x) isRand [4,1),respectively.

1. (a)Letg(x) = 2f(2x4) + 1. Draw the graph ofg(x). Make sure to clearly label where the three labeled points on the graph off(x) are translated to ong(x).
2. (b)Give the domain and range ofg(x).
3. (c)Suppose we restrict the domain off(x) to [2,8]. Draw the graph off1(x). Again, make sure to clearly label the points on your drawing that correspond to the labeled points in this domain.
4. (d)Give the domain and range off1(x).
5. (e)What property does the restricted domain version offfrom part (c) have that allows us to define the inverse as a function?

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