Inverse Functions
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Inverse Functions

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    Inverse Functions Inverse Functions Presentation Transcript

      • To have an inverse function , the function must:
        • Be one-to-one
        • Pass the horizontal line test
      • Otherwise the inverse is a relation
    • 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