Show That The Function F X 2 3 X Is One To One Check You Answer Algebraically

1. Show that the function f(x) = 2 / 3 – x is one-to-one. Check you answer algebraically and graphically. Verify that the range of f is the range of f -1 and viceversa.

2. x = 1/x, g(x) = x^2, and h(x) = sqrt(2x)

a) Find and simplify the expression for the function (h of f of g)(x)

b) State the domain of the expression you just found using interval notation

3. Ben paddles his kayak at twice the speed of the current in the James River. If he paddles upriver for 3 hours, how long will the return trip downriver take? Note: The upriver trip is against the current, and downriver is with the current. The distance in each direction is the same.

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