vb.net generate qr code Finding an Inverse Relation in VS .NET

Printer ANSI/AIM Code 39 in VS .NET Finding an Inverse Relation

Finding an Inverse Relation
Code 39 Full ASCII Decoder In .NET
Using Barcode Control SDK for Visual Studio .NET Control to generate, create, read, scan barcode image in VS .NET applications.
Code 39 Full ASCII Creator In Visual Studio .NET
Using Barcode maker for .NET framework Control to generate, create Code39 image in Visual Studio .NET applications.
Replacing y by g 1(x), we get g 1(x) = x 2 The domain of the original relation g spans the set of nonnegative reals, and the range of g spans the set of all reals Therefore, the domain of g 1 includes all reals, while the range of g 1 is confined to the set of nonnegative reals
Code-39 Decoder In .NET Framework
Using Barcode scanner for .NET Control to read, scan read, scan image in Visual Studio .NET applications.
Draw Bar Code In .NET Framework
Using Barcode maker for VS .NET Control to generate, create bar code image in VS .NET applications.
Still another example Let s find the inverse of the relation
Recognizing Barcode In .NET Framework
Using Barcode reader for Visual Studio .NET Control to read, scan read, scan image in Visual Studio .NET applications.
Drawing Code 3/9 In Visual C#.NET
Using Barcode printer for Visual Studio .NET Control to generate, create Code39 image in .NET framework applications.
h(x) = x 1/2 When we write the 1/2 power of a quantity without including any sign, we mean the nonnegative square root of that quantity If we call the dependent variable y, then we have y = x1/2 Swapping the names of the variables, we get x = y1/2 Squaring both sides, we obtain x2 = y Reversing the left- and right-hand sides of this equation yields y = x2 Replacing y by h 1(x), we get h 1(x) = x 2 Is the inverse of h identical to the inverse of g we obtained a few moments ago It looks that way on the surface, but it s not so simple when we examine the situation more closely The domain of h spans the set of nonnegative reals, just as the domain of g does But the range of h spans the set of nonnegative reals only (not the set of all reals, as the range of g does) Transposing, we must conclude that the domain and range of h 1 are both confined to the set of nonnegative reals The relations h and h 1 are therefore restricted versions of g and g 1
Paint USS Code 39 In Visual Studio .NET
Using Barcode maker for ASP.NET Control to generate, create Code39 image in ASP.NET applications.
ANSI/AIM Code 39 Creation In Visual Basic .NET
Using Barcode generator for VS .NET Control to generate, create USS Code 39 image in VS .NET applications.
The graphical way Imagine the line represented by the equation y = x in the Cartesian xy plane as a point reflector For any point that s part of the graph of the original relation, we can locate its
EAN / UCC - 13 Maker In VS .NET
Using Barcode creation for VS .NET Control to generate, create GTIN - 128 image in VS .NET applications.
Generating ANSI/AIM Code 39 In .NET
Using Barcode maker for VS .NET Control to generate, create Code-39 image in VS .NET applications.
Inverse Relations in Two-Space
GTIN - 13 Generator In .NET Framework
Using Barcode encoder for Visual Studio .NET Control to generate, create EAN-13 image in .NET framework applications.
Make Code 93 In .NET
Using Barcode maker for VS .NET Control to generate, create Code 93 image in .NET applications.
y 6 4 Inverse Original 2 y=x Original Point reflector line Inverse
Bar Code Recognizer In Java
Using Barcode Control SDK for BIRT Control to generate, create, read, scan barcode image in BIRT applications.
Universal Product Code Version A Maker In Visual Basic .NET
Using Barcode encoder for Visual Studio .NET Control to generate, create UPC-A Supplement 2 image in Visual Studio .NET applications.
x 6 Inverse 4 2 2 Original 4 6 Original Inverse 2 4 6
Decode Bar Code In Visual Basic .NET
Using Barcode Control SDK for .NET Control to generate, create, read, scan barcode image in Visual Studio .NET applications.
GTIN - 13 Reader In Java
Using Barcode scanner for Java Control to read, scan read, scan image in Java applications.
Figure 12-1
UCC.EAN - 128 Printer In Java
Using Barcode creation for Eclipse BIRT Control to generate, create GTIN - 128 image in BIRT reports applications.
Code 39 Reader In None
Using Barcode reader for Software Control to read, scan read, scan image in Software applications.
Any point on the graph of the inverse of a relation is the point s image on the opposite side of a point reflector line The new coordinates are obtained by reversing the sequence of the ordered pair representing the original point
Create Barcode In None
Using Barcode maker for Office Excel Control to generate, create bar code image in Excel applications.
Data Matrix 2d Barcode Maker In None
Using Barcode generator for Excel Control to generate, create Data Matrix ECC200 image in Microsoft Excel applications.
counterpart in the graph of the inverse relation by going to the opposite side of the point reflector, exactly the same distance away Figure 12-1 shows how this works The line connecting a point in the original graph and its mate in the inverse graph is perpendicular to the point reflector The point reflector is a perpendicular bisector of every point-connecting line Mathematically, we can do a point transformation of the sort shown in Fig 12-1 by reversing the sequence of the ordered pair representing the point For example, if (4,6) represents a point on the graph of a certain relation, then its counterpoint on the graph of the inverse relation is represented by (6,4) When we want to graph the inverse of a relation, we flip the whole graph over along a hinge corresponding to the point reflector line y = x That moves every point in the graph of the original relation to its new position in the graph of the inverse Figures 12-2, 12-3, and 12-4 show how this process works with the three relations we dealt with a few moments ago The positions of the x and y axes haven t changed, but the values of the variables, as well as the domain and range, have been reversed
Finding an Inverse Relation
y 6 4 2 (0, 2) x 6 ( 5, 3) 4 6 4 2 2 2 4 6 (4, 6)
y 6 (6, 4) 4 2 (2, 0)
6 4 2 2 4 ( 3, 5) 2 4 6
Figure 12-2
At A, Cartesian graph of the relation y = x + 2 At B, Cartesian graph of the inverse relation
Inverse Relations in Two-Space
y 6 (1, 1) 4 (0, 0) 2 (4, 2)
6 4 2 2 (4, 2) 4 (1, 1) 6 2 6
y 6 ( 2, 4) ( 1, 1) 2 (2, 4) (1, 1) x 6 4 (0, 0) 4 6 2 2 2 4 6
Figure 12-3
Copyright © OnBarcode.com . All rights reserved.