Post1o5_1330 - 1-f is A. Example 4: Determine if 2 5 ) (-=...

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Math 1330 Class Notes – Section 1.5, Page 1 of 4 Math 1330 - Section 1.5 Inverse Functions We’ll start by reviewing one-to-one functions . A function is one-to-one if it passes the Horizontal Line Test (HLT). The Horizontal Line Test: A function is one-to-one if any horizontal line intersects the graph of the function in no more than one point. Example 1: Determine if the functions graphed are one-to-one. Example 2: Determine if 3 ) ( 2 + = x x f is one-to-one. Example 3: Determine if 2 ) ( 3 - = x x f is one-to-one.
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Math 1330 Class Notes – Section 1.5, Page 2 of 4 The inverse function of a one-to-one function is a function ) ( 1 x f - such that ( 29 ( 29 . 1 1 x f f f f = = - - o o To determine if two functions are inverses of one another, you need to compose the functions in both orders. Your result should be x in both cases. That is, given two functions f and g , the functions are inverses of one another if and one if . )) ( ( )) ( ( x x f g x g f = = Note that if A is the domain of f and B is the range of f , then the domain of 1 - f is B and the range of
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Unformatted text preview: 1-f is A. Example 4: Determine if 2 5 ) (-= x x f and 5 2 5 1 ) (-= x x g are inverses of one another. Example 5: Determine if , 1 ) ( 2 + = x x x f and 1 ) (-= x x g are inverses of one another. Math 1330 Class Notes Section 1.5, Page 3 of 4 You need to be able to find the inverse of a function. Follow this procedure to find an inverse function: 1. Rewrite the function as ). ( x f y = 2. Interchange x and y . 3. Solve the equation you wrote in step 2 for y . 4. Rewrite the inverse using inverse notation, ). ( 1 x f-Example 6: You know that 7 4 ) (-= x x f is a one-to-one function. Find its inverse. Example 7: Determine if 5 , ) 5 ( ) ( 2 -= x x x f is a one-to-one function. If it is, find its inverse. Math 1330 Class Notes Section 1.5, Page 4 of 4 Example 8: x x x f-+ = 2 1 ) ( is a one-to-one function. Find its inverse. Example 9: If ) 1 ( , 2 ) 1 ( 1 =-=--f f and , 5 ) 2 ( = f find ) ( f and ) 5 ( 1-f ....
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Post1o5_1330 - 1-f is A. Example 4: Determine if 2 5 ) (-=...

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