MATH 109 Midterm: Math 109-Winter 2015-Exam 2 Solutions
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Math 109 winter 2015 midterm 2 sample solutions. For each part, decide if the statement is true or false, and prove that your answer is correct. (a) (5 pts). X r, y r, x + y < 0. (b) (5 pts). X r, y r, x + y < 0. Given any x r, choose y = x 1. Then taking y = x + 1, we must have x + y < 0. But x + y = x + ( x + 1) = 1 > 0, a contradiction. Let r = r \ {0} be the set of all nonzero real numbers. Consider the function f : r r de ned by f (x) = 2/x. Find a formula for its inverse function f 1 and justify that your formula is correct. We need to show that f is both injective and surjective. R and that f (x1) = f (x2).