Fall 2006 - Egger's Class - Exam 1 (Version 2)

Fall 2006 - Egger's Class - Exam 1 (Version 2) - Math 20A...

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Math 20A Midterm Exam 1 (version 2) Solution 1. (6 points) Let f ( x ) = e 3 x and g ( x ) = 3 ln( x ). (a) Find the domain and range of f ( x ). The domain of f is R , the set of all real numbers and the range of f is (0 , ), the set of all positive real numbers. (b) Does f ( x ) have an inverse function? Justify your answer. Yes, f ( x ) has an inverse function because it is an increasing function, hence one-to-one. (c) Are the functions f ( x ) and g ( x ) inverses of each other? Explain how you determined your answer. No: g ( x ) is not the inverse of f ( x ) since f ( g ( x )) = e 3 g ( x ) = e 3 · 3 ln( x ) = x 9 n = x . (Note: it would be just as good to observe that g ( f ( x )) n = x .) 2. (6 points) For each of the following limits, either evaluate it or explain why it does not exist. (a) lim x 0 b 1 3 x - 1 x ( x + 3) B lim x 0 1 3 x 1 x ( x + 3) f = lim x 0 ( x + 3) 3 3 x ( x + 3) = lim x 0 x 3 x ( x + 3)
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This note was uploaded on 04/24/2008 for the course MATH 20A taught by Professor Staff during the Fall '08 term at UCSD.

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Fall 2006 - Egger's Class - Exam 1 (Version 2) - Math 20A...

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