4.1 Use the definition of inverses to determine whether f and g are inverses. 1. f x 4 x 2, g(x)= 1 x2 4 If the function is defined as a one-to-one, (a) write an equation for the inverse function in the form , (b) graph f and f on the same axes, and (c) give the domain and the range of y f 1 x and 2. f 1 . If the function is not one-to-one say so. f x x3 2 Graph each function. 3. Pick the correct graph. x 4. 5 f x 3 A f 1 x 1 f x 6 B C D E F Use the properties of logarithms to rewrite each expression. Simplify the result if possible. Assume all variables represent positive real numbers. 5. log 3 4p q Use the change-of -base theorem to find an approximation to four decimal places for each logarithm. 6. log8 0.71 Solve the logarithmic equation. Express all solutions in exact form. 7. ln 5 4 x ln 3 x ln 3 8. Decay of Iodine How long will it take any quantity of iodine-131 to decay to 25% of its initial amount, knowing that it decays according to the exponential function A t A0 e 0.087 t , where t is time in days