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quiz3Asol - Solutions to Quiz 3A www.math.u.edu/harringt 1...

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Solutions to Quiz 3A www.math.ufl.edu/˜harringt January 24, 2008 1. Find the exact value of each expression: (a) log 5 125 = log 5 5 3 = 3 log 5 5 = 3 (b) ln(1 /e ) = ln(1) - ln( e ) = 0 - 1 = - 1 2. Find the inverse of f ( x ) = 3 - e 2 x and find the range of f - 1 . (a) First we will find the inverse function. f ( x ) = y = 3 - e 2 x x = 3 - e 2 y x 2 = 3 - e 2 y x 2 - 3 = - e 2 y 3 - x 2 = e 2 y ln(3 - x 2 ) = 2 y 1 2 ln(3 - x 2 ) = y f - 1 ( x ) = 1 2 ln(3 - x 2 ) (b) Next we will find the range of f - 1 by finding the domain of f . Recall that the range of f - 1 is the same as the domain of f . Since f ( x ) = 3 - e 2 x then we need to find when 3
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