MAT102H5 Study Guide - Quiz Guide: Er1 Electric Trainset, Natural Number
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MAT102H5 Full Course Notes
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Mat102f - intro. to mathematical proofs - fall 2012 - utm. Quiz 2 (version b) - october 5, 2012 solutions: consider the following subsets of r: (4 marks) B = (1, 4) and the function f : r r , Compute the following sets (you can use only the symbols { , }, , and the interval notation). f (x) = |x|. No explanation is needed. (a) a b = (1, 2] (b) a b = [0, 2] (cid:8)1, 2(cid:9) (g) f (a n) = (h) f (a b) n = (cid:8)1, 2, 3(cid:9). 2: consider the function f : (0, ) r , Prove that the image of f is the interval(cid:0)0, 1. Do not use calculus! f (x) = x. Take y f(cid:0)(0, )(cid:1), which satis es y = f (x) for some x (0, ). We want to prove that 0 < y < 1. 2 (because 2x + 1 > 0) (always true!)
