P05 - f ( x ) = x 2 + √ x +2. What is its domain? Write...

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Project 5 MAC 2311 1. Examine the function g ( x ) = 1 - 2ln( x - 1). Find the x - and y -intercepts of g ( x ), if any, and write a formula for the inverse function g - 1 ( x ). Using the above information only, what are the x - and y -intercepts of g - 1 ( x ), if any? Sketch both g ( x ) and g - 1 ( x ) on the axes below, labelling any asymptotes and intercepts. 2. Examine the function, h ( x ) = 2 - ln( x + 1) 1 - e x , and find its domain. Then, show it is possible for h ( x ) to take the value - 1 but not 2. (Suppose it can, and show it would require the intersection of shifted graphs of ln( x ) and e x , which you know how to draw.) Think about this: given some function f ( x ) and number a , how is solving the equation f ( x ) = a related to finding f - 1 ( a ); what is the important di±erence (consider sin( x ))? So why must a function be one-to-one to have an inverse, and why do we find the inverse by solving for x ?
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3. Examine the one-to-one function
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Unformatted text preview: f ( x ) = x 2 + √ x +2. What is its domain? Write the range of f-1 ( x ) in interval notation. Compute the value f-1 (4). Which of these numbers is NOT in the domain of the function f-1 and why? , 1 , 2 , 4 , 5 Note: if you have trouble making a decision about ”5” that is all right. You could consult a graph of f ( x ), use an equation solver, or use intermediate value theorem, which we will discuss in Lecture 8; the idea is to make you think about it after figuring out the other four using algebra or by trying some simple guesses. .. 3. Solve the following logarithmic equation: log( x + 4)-log(1 + √ x ) = 1 2 log( x ) . Now solve the equation: log(4-x )-log(1-√ x ) = 1 2 log( x ) ....
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This note was uploaded on 01/13/2010 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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P05 - f ( x ) = x 2 + √ x +2. What is its domain? Write...

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