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Inverse Functions

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Inverse Functions

1. 1. <ul><li>To have an inverse function , the function must: </li></ul><ul><ul><li>Be one-to-one </li></ul></ul><ul><ul><li>Pass the horizontal line test </li></ul></ul><ul><li>Otherwise the inverse is a relation </li></ul>
2. 2. Domain of the function = Range of the inverse Range of the function = Domain of the inverse Example:
3. 3. The reflection of a point (a,b) about the x-axis is (a,-b) The reflection of a point (a,b) about the y-axis is (-a,b) Original and inverse are symmetric over the line y=x
4. 4. Write original function. Replace f(x) by y. Interchange x and y. Multiply each side by 5. Isolate the y-term Solve for y. Replace y by f -1 ( x ).
5. 5. Function Not a function
6. 6. One-to-one function Not a one-to-one function