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Inverse Functions: Determining, Finding and Graphing

Learn how to determine if two functions are inverses, find the inverse of a function, graph inverse functions, and determine if a function is one-to-one.

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Inverse Functions: Determining, Finding and Graphing

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  1. MAT 150 AlgebraClass #14 Topics: Determine if two functions are inverses Determine if a function is one-to-one Find and graph the inverse of a function Find the inverse functions on limited domains .

  2. Inverse Functions Functions f and g for which for all x in domain of g and for all x in the domain of f are called inverse functions. In this case, we denote g by , read as “f inverse.” NOTE:

  3. One-To-One Functions We can show a function has an inverse if it is a one-to-one function. One-to-one: _________________________________________ __________________________________________________. This statement means that for a one-ton-one function

  4. One-to-one functions Determine if each of the functions is a one-ton-one function.

  5. _________________Test NOTE: ____________________________________________________________________________________________________. A function is one-to-one if no _____________can intersect the graph of the function in more than one point. FAILED PASSED

  6. Inverse functions • Determine if has an inverse function. • Verify that is the invers function of • Find the domain and range of each function.

  7. Finding the Inverse of a function • Rewrite the equation replacing f(x) with y. • Interchange x and y in the equation defining the function. • Solve the new equation for y. If this equation cannot be solved uniquely for y, the original function has no inverse function. • Replace y with .

  8. Find the inverse function . Graph both f(x) and its inverse of the same axes.

  9. Graphs of Inverse Functions The graphs of a function and its inverse are ___________ with respect to the line y = _____.

  10. Assignment Pg. 283-287 #1-9 odd #23-31 odd #34,45,49

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