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Understanding Inverse Functions - Texas Tech University

Explore the concept of inverse functions as taught by the Department of Mathematics & Statistics at Texas Tech University. Learn the definition, properties, and graphing methods of inverse functions showcased through examples and problem-solving.

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Understanding Inverse Functions - Texas Tech University

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  1. Inverse Functions Property of Texas Tech University Department of Mathematics & Statistics

  2. Recall A function is a rule that sends to . Now we want to reverse this process.

  3. Inverse Functions An inverse function for is a function (x) so that and

  4. CAUTION! is NOT the same as If then . Note and

  5. A Problem So if we try to “go backwards” from 4, should we go back to 2 or to -2?

  6. Definition A function is one-to-one if implies So every is the image of a unique

  7. Horizontal Line Test A function is one-to-one if and only if its graph intersects horizontal lines no more than once

  8. Graphing Inverse Functions

  9. Example Solution

  10. Inverse Trig Functions Notice that the trig functions are definitely not one-to-one, but if we cut back their domains, the restricted functions will be.

  11. Inverse Trig Functions Trig functions take an angleand give you back a number. Inverse trig functions take a number and give you back an angle.

  12. Example Solution

  13. Example Solution

  14. Example Solution

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