Mathematics Dictionary
Dr. K. G. Shih
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Mathematics Dictionary Dr. K. G. Shih |
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Contents
of Mathematics Dictionary Program WebABC Applications of Mathematics Dictionary on Internet Graphic Samples of Mathematics Dictinary |
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Subject :
Intersection of Linear Function with its Inverse Q1. What is the inverse of a function A1. The defintion is
* It is the image of Y = F(X) about Y = X * Function y = x looks like an mirror Q2. Expression of inverse of y = F(x) = a*x+b A2. Inverse of Y = a*x+b is X = a*y+b
* Interchange x and y we have * The inverse is y = (x-b)/a * Express x in terms of y * The inverse is x = a*y + b Q3. Proof inverse is x=a*y + b A3. Proof
* Hence x-b = a*y * Hence x = a*y+b Q4. Properties of inverse function A4. Let y=F(x) and inverse y=G(x)
* G(F(x)) = x Q5. Example : Prove F(G(x))=x A5. Proof
* F(G(x))=a*(G(x))+b * F(G(x))=a*((x-b)/a) + b = x Q6. How How many intersctions of y = a*x+b with its inverse A6. Graphic solutions Program ABH
* There is one intersection Q7. How to find intersections ? A7. Find intersection of y = a*x + b with inverse
* It must intersect with y=x * Hence we solve y = a*x + b and y = x first * This gives a quadratic equation : a*x + b = x Q8. When is there no intersection ? A8. Answer
* Since the line is parallel to y=x Examples Example 1 : Use Program ABH to view the diagrams
* y = 2 * x = 2 |
Remarks
* The system is easy in use and gives thousands applications * On this website only some samples are given for demonstration * You should have it on your computer * Then you can use your computer as a graphic calculator * Also you can find many mathematical patterns for school wook * For more information, Please contact Dr. K. G. Shih * Visit the URL to see more samples * Visit the URL to view 105 graphic samples in Program WebABC * You can download it and Click file WebABC will run |
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