Unformatted text preview: Math 55 Worksheet Adapted from worksheets by Rob Bayer, Summer 2009. Functions 1. Find the value of ∑ 3 i =1 ∑ 3 j =1 ( i j ) 2. Determine whether each of the following are injections, surjections, bijections, or none of the three. (a) f : R → R ,f ( x ) = 3 x 2 (b) f : R → Z ,f ( x ) = b x c (c) f : N → N ,f ( n ) = n + 1 (d) f : R → R ,f ( x ) = x ( x 3)( x + 2) 3. Write down the formal definitions of a function , injectivity and surjectivity . These will help with problem ?? . 4. Decide whether each of the following are true or false. For those that are true, prove it. For those that are false, provide a counterexample. (a) If f and g are injective, then so is f ◦ g . (b) If f and g are surjective, then so is f ◦ g . (c) If g ◦ f is injective, then so is f . (d) If g ◦ f is injective, then so is g . (e) If f is not surjective, then g ◦ f is not surjective. 5. Explain why noninjective functions have no inverse function 6. The Hotel Infinity is rather unique, in that it has infinitly many rooms, one for each natural number. However,6....
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This note was uploaded on 02/06/2012 for the course MATHEMATIC 55 taught by Professor Robbayer during the Summer '09 term at Berkeley.
 Summer '09
 RobBayer
 Math

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