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y = (25 x 2)1/2 Swapping the names of the variables, we get x = (25 y 2)1/2 Squaring both sides, we obtain x 2 = 25 y 2 Subtracting 25 from each side yields x 2 25 = y 2 When we multiply through by 1 and transpose the left-hand and right-hand sides of the equation, we obtain y 2 = 25 x 2 Taking the complete square root of both sides gives us y = (25 x 2)1/2 Replacing y by f+ 1(x) to indicate the inverse of f+, we get f+ 1(x) = (25 x 2)1/2 Does this look like the same thing as the inverse of the original relation f Don t be fooled; it isn t the same! We haven t quite finished our work We must transpose the domain and range of f+ to get the domain and range of the inverse relation f+ 1 The domain of f+ is the closed interval [ 5,5], and the range of f+ is the closed interval [0,5] Therefore, the domain of f+ 1 is the closed interval [0,5], and the range of f+ 1 is the closed interval [ 5,5] Figure 12-9A is a graph of this inverse relation It s easy to see that f+ 1 fails the vertical-line test, so it s not a true function of x

What about the inverse of f- Now let s go through the algebra to figure out the inverse of the function f This process is almost identical to the work we just finished, but it s a good practice to carry it out step by step anyway If we call the dependent variable y, then

F2, %

In this section, we o er three tools that were mentioned above: the known problems and issues tracking document; the pilot test lessons learned document; and a method for creating an accurate test schedule.

y = (25 x2)1/2

6 4 2 2 4 6 2 4 6

The known problems and issues tracking document is an excellent tool for any project in transition to production and also for any time when there is a crisis or a lot is happening all at once and we are not sure what is going on I created it during one project s transition stage I already had a to-do list, but it just was not working: I was not keeping up with all that was going on I evaluated the to-do list and I realized that it did not work because it did not re ect the di erent types of tasks of which I needed to keep track So I created a separate category for each type of task, and a di erent table to track the information needed to manage that type of task.

6 4 2 2 4 6 2 4 6

Figure 12-9

FIG 9.13. By proper choice of coordinates, speed contours for a centrifugal pump are made into straight lines.

At A, Cartesian graph of the inverse of the function y = (25 x 2)1/2 At B, Cartesian graph of the inverse of the function y = (25 x 2)1/2 Vertical-line tests indicate that neither of these inverse relations is a function

You can build your own open issues tracking document using a word processor or spreadsheet For each item, include an initial entry date, a deliverable, the person who will do the work, and a delivery date You can set up six sections, one to track each of the following types of items: Decisions still to be made Track what the question is, who should decide, and what should be delivered with the answer Recently resolved decisions Track who should be informed and what actions should be taken Work that needs to be done Track the deliverable This is for items where the job is de ned and you can estimate how long the work will take Problems that need to be solved This is for items where you need to do diagnosis, and you do not know exactly what work will be done or how long it will take.