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Understanding Inverse Functions: Concepts and Examples

Learn how to find inverse functions step by step, including definitions, domain adjustments, and graphical representation. Practice finding inverse functions for various given functions. Understand the concept of one-to-one functions.

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Understanding Inverse Functions: Concepts and Examples

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  1. Practice #9 p. 231 3-27 eoo Find when

  2. Inverse functions - one function undoes the other. x f(x) 0 -3 1 -1 2 1 3 3 x g(x) -3 0 -1 1 1 2 3 3 Definition of Inverse Functions - If functions f and g are such that for all x in the domains of f and g , then the f and g functions are said to be inverses of each other.

  3. Finding an inverse function: 1. Rewrite the function in y= form 2. Switch x and y 3. Solve for y 4. Adjust the domain of the original function if necessary 5. The new function is

  4. Find the inverse of each function.

  5. Pre calculus Problem of the Day Homework: p. 221 99-102 all, p. 231-232 29-63 odds, 67, 68 Use functions f and g to find the indicated domains or functions. Domain of f+g, f-g, and fg. Domain of f/g. c) f(g(x)) d) Domain of f(g(x)). [ 1, 2)U(2, ∞) ( 1, 2)U(2, ∞) c) d) [ 1, 5)U(5, ∞)

  6. Find the inverse for each function. Sketch the original and its inverse on the same graph for each function.

  7. One-to-one functions- all x values have unique y answers and If a function is one-to-one its inverse will also be a function without limiting the domain. A function is one-to-one if it passes the horizontal line test.

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