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Notice that ref precedes the entire parameter declaration in the method and that it precedes the argument when the method is called The output from this program, shown here, confirms that the value of the argument, a, was indeed modified by Sqr( ):

a before call: 10 a after call: 100

= 55 = 100 = 2 = 314

Using ref, it is now possible to write a method that exchanges the values of its two value-type arguments For example, here is a program that contains a method called Swap( ) that exchanges the values of the two integer arguments with which it is called:

Jane K Cleland is the author of Business Writing for Results Have you seen A Funny Thing Happened on the Way to the Forum on Broadway

// Swap two values using System; class ValueSwap { // This method now changes its arguments public void Swap(ref int a, ref int b) { int t;

Part I:

.

t = a; a = b; b = t; } } class ValueSwapDemo { static void Main() { ValueSwap ob = new ValueSwap(); int x = 10, y = 20; ConsoleWriteLine("x and y before call: " + x + " " + y); obSwap(ref x, ref y); ConsoleWriteLine("x and y after call: " + x + " " + y); } }

The output from this program is shown here:

x and y before call: 10 20 x and y after call: 20 10

Here is one important point to understand about ref: An argument passed by ref must be assigned a value prior to the call The reason is that the method that receives such an argument assumes that the parameter refers to a valid value Thus, using ref, you cannot use a method to give an argument an initial value

17 For each of the following pairs of functions, calculate f g and g f g (x) = (x + 1)2 (a) f (x) = x 2 2x (b) f (x) = x 1 g (x) = x 2 + 2 2 (c) f (x) = sin(x x ) g (x) = cos(x 2 + x) g (x) = ln(x + 3) (d) f (x) = e x 2 2 (e) f (x) = sin(x x) g (x) = ln(x 2 + 2x) 2 g (x) = e 2x (f) f (x) = e x (g) f (x) = x(x 1)(x + 3) g (x) = (2x 1)(x + 2) 18 Consider each of the following as functions from R to R and say whether the function is invertible If it is, find the inverse with an explicit formula (a) f (x) = x 3 + 1 (b) g (x) = x 2 + x (c) h(x) = sgn x |x|, where sgn x is +1 if x is positive, 1 if x is negative, 0 if x is 0 (d) f (x) = x 3 8 (e) g (x) = e 3x (f) h(x) = cos x (g) f (x) = cot x (h) g (x) = sgn x x 2 , where sgn x is +1 if x is positive, 1 if x is negative, 0 if x is 0 19 For each of the functions in Exercise 18, graph both the function and its inverse in the same set of axes 20 Determine whether each of the following functions, on the given domain S, is invertible If it is, then find the inverse explicitly S = [1, 7] (a) f (x) = x 3 , (b) g (x) = ln x, S = [5, 10] (c) h(x) = cos x, S = [0, /2] (d) f (x) = sin x, S = [0, ] (e) g (x) = cot x, S = [ /2, 0] 2 S = [ 1, 1] (f) h(x) = x , (g) f (x) = x 2 + x, S = [2, 5].