# P03 - Project 3 MAC 2311 1 For a function f and number a...

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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 ? 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) . 2. Solve the logarithmic equations. Why does one yield a false solution? log(4+ x ) - log(1+ x ) = 1 2 log( x ) log(4 - x ) - log(1 - x ) = 1 2 log( x )

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3. When resistors having resistance r and R
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