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Understanding Inverse Functions in Mathematics

This explanation explores inverse functions in mathematics using a walking distance analogy, comparing domains and ranges, composite operations, and more.

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Understanding Inverse Functions in Mathematics

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  1. Inverse Functions • Consider a person walking, where time is calculated in seconds, and distance is calculated in feet.

  2. In table form, the function might look like the following:

  3. Now consider another function related to the first.

  4. In table form, the function g is given below:

  5. We say that function g is the inverse of function f.

  6. Compare the Domain and Range of the two functions. • Domain f = Range g • Range f = Domain g

  7. Notice the relationship of x-values and function values. • f (3)=30 • g (30)=3

  8. Composite operation with inverses. • f (g(30)) =f(3) =30

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