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[object Object],[object Object],[object Object],[object Object]
Domain of the function = Range of the inverse Range of the function = Domain of the inverse Example:
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
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 ).
Function Not a function
One-to-one function Not a one-to-one function

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Inverse Functions

  • 1.
  • 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