1. a. Let x = (y + 1)/(y - 1). Solve for y and you have the inverse:

x(y - 1) = y + 1 => xy - x = y + 1 => xy - y = x + 1 => y(x - 1) = x + 1 => y = (x + 1)/(x - 1).

In other words, f is its own inverse: fof(x) = x. Such a function is called an involution.

b. Let x = (2y + 3)/(3y - 2). Solve for y and you have the inverse. Proceed as above.

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2. a. What is the necessary condition for fog to be defined? Test this condition for f.

b. fof(x) = (f - 3)/(2f - 1) = .

The penultimate expression is obtained by multiplying top and bottom by (2x - 1).

c. Use the above result, ie. fof(x) = x.

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3. ((x-4)/3)^2= x+2 => (x - 4)^2 = 9(x + 2). Expand the left hand side, re-arange and simplify to get:

quadratic = 0.

Solve the quadratic.