Assignment 9

1. Let . Simplify each of the following, graph, and determine the domain.

a. f(f(x))

b. f(g(x))

c. g)f(x)

d. f)g)g(x)

2. A rope is tied to the bow of a boat, 3 feet lower than a loop on a dock. The rope runs through the loop.

a. Find the distance from the boat to the dock as a function of the length of the rope from the loop to the boat.

b. Now, if the length of rope is 10 – 2*t, find the position of the boat as a function of t.

3. You know the volume and surface area of a sphere as a function of the radius. Find the radius as a function of volume, and use this to get surface area as a function of volume.

4. Sketch the function sin(x). Is this an invertible function? Restrict the range so that you have something invertible, and sketch the inverse on the same graph.

5. Repeat the above for tan(x), and .

6. Let . Let a = 0.5 and choose some starting x0 in the interval ( –1, 1). Let x1 be q(x0). Then x2 = q(x1). Keep going. What do you see? (Use a calculator on these.)

7. Repeat the above for a = 1.1, and 1.3.