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SOLUTION First we square t and add 3, then we divide 2 by the quantity just obtainedAs a result, we de ne f (t) = t 2 +3 and g(t) = 2/t It follows that r(t) = (g f )(t) You Try It: Express the function g(x) = 3/(x 2 + 5) as the composition of two functions Can you express it as the composition of three functions

Any code that uses pointers must be marked as unsafe by using the unsafe keyword You can mark types (such as classes and structures), members (such as methods and operators),

Part I:

FIGURE 1017 Roller follower constructed of standard needle bearings with laminated thermoset resin outer race

or individual blocks of code as unsafe For example, here is a program that uses pointers inside Main( ), which is marked unsafe:

// Demonstrate pointers and unsafe using System; class UnsafeCode { // Mark Main as unsafe unsafe static void Main() { int count = 99; int* p; // create an int pointer p = &count; // put address of count into p ConsoleWriteLine("Initial value of count is " + *p); *p = 10; // assign 10 to count via p ConsoleWriteLine("New value of count is " + *p); } }

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Let f be the function which assigns to each working adult American his or her Social Security Number (a 9-digit string of integers) Let g be the function which assigns to each working adult American his or her age in years (an integer between 0 and 150) Both functions have the same domain, and both take values in the nonnegative integers But there is a fundamental difference between f and g If you are given a Social Security number, then you can determine the person to whom it belongs There will be one and only one person with that number But if you are given a number between 0 and 150, then there will probably be millions of people with that age You cannot identify a person by his/her age In summary, if you know g(x) then you generally cannot determine what x is But if you know f (x) then you can determine what (or who) x is This leads to the main idea of this subsection Let f : S T be a function We say that f has an inverse (is invertible) if there is a function f 1 : T S such that (f f 1 )(t) = t for all t T and (f 1 f )(s) = s for all s S Notice that the symbol f 1 denotes a new function which we call the inverse of f Basic Rule for Finding Inverses To nd the inverse of a function f , we solve the equation (f f 1 )(t) = t for the function f 1 (t) EXAMPLE 140

considerable amount of detrimental sliding Some of the factors are a jammed or dirty bearing race, uctuations in the cam peripheral speed (especially in starting and stopping), backlash, misalignment, and the proportions of the positive-drive grooved roller follower, if used Let us discuss these conditions, assuming that the roller is running properly on the cam surface, ie, with its bearing lubricated and free of contaminants The peripheral speed of a cam rotating at a constant speed, or starting and stopping, is continuously changing This alternately accelerates and decelerates the cam roller, inducing a torque reaction that for pure rolling (Fig 1019) must be less than the moment of the static frictional force Thus Ia < m s FRr (107)

The output of this program is shown here:

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