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P03SelectedAnswers - Project 3 MAC 2311 1. For a function f...

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Project 3 MAC 2311 1. For a function f and number a , how is solving the equation f ( x ) = a related to finding f - 1 ( a ) ; what is the important difference (consider sin( x ) )? What property must the function have? 2. Examine the function f ( x ) = x 2 + x . What equation must hold in order for 15 to be in the range of f ? How is this question related to the intersection of the graph of x with the parabola 15 - x 2 ? Consider the intersection of the graph of x with parabolas of the form A - x 2 . Use them to convince yourself that f ( x ) is one-to-one and that 15 is in the range of f . What seems to be the range of f ? What does this tell you about the domain of f - 1 ? try sketching y = x and several parabolas of form y = A - x 2 Is it easy to write the inverse function f - 1 ( x ) ? Compute f - 1 (2) and f - 1 (18) nonetheless. Using trial and error with a calculator, find a number that is very close to being f - 1 (15) . e.g.,
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This note was uploaded on 04/04/2012 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

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P03SelectedAnswers - Project 3 MAC 2311 1. For a function f...

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