hw4solutions

hw4solutions - 24 For the function to be invertible it must...

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SOLUTIONS TO HOMEWORK #4 (Total Point: 40) Section 2.3: 2, 24, 40 (10 points) Total Points: 30 2. a) This is not a function because the rule is not well defined. We do not know whether f(3) = 3 or f(3) = -3. For a function it cannot be both at the same time. b) This is a function. For all integers n, √ (n 2 + 1) is a well-defined real number. c) This is not a function with domain Z, since for n=2 (and also for n= -2) the value of f(n) is not defined by the given rule. In other words, f(2) and f(-2) are not specified since division by 0 makes no sense.
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Unformatted text preview: 24.) For the function to be invertible, it must be a one to one correspondence. This means that it has to be one-to-one, which it is, and onto, which it is not, because, its range is the set of positive real numbers, rather than the set of all real numbers. When we restrict the codomain to be the set of positive real numbers, we get an invertible function. In fact, there is a well-known name for the inverse function in this case-the natural logarithmic function (g(x) = ln x). Section 2.4: 20 (10 points) Total Points: 30...
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