To have an inverse function, a function must be one-to-one and pass the horizontal line test. If a function fails either of these, the inverse is considered a relation instead of a function. The domain of the original function becomes the range of the inverse, and the range of the original becomes the domain of the inverse. An example given is reflecting points across the x or y-axis.

2. Domain of the function = Range of the inverse Range of the function = Domain of the inverse Example:

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. 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. Function Not a function

6. One-to-one function Not a one-to-one function