Ch 2.3 Inverse Functions.pdf - CHAPTER 2 GRAPHS AND FUNCTIONS 2018-2019 WS CH 2.3 Inverse Functions 1 ONE TO ONE FUNCTION THEIR INVERSES Let’s compare

# Ch 2.3 Inverse Functions.pdf - CHAPTER 2 GRAPHS AND...

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2018-2019 1 WS CH 2.3 Inverse Functions CHAPTER 2 GRAPHS AND FUNCTIONS
2018-2019 WS CH 2.3 Inverse Functions 2 Let’s compare the function ? and g ONE TO ONE FUNCTION & THEIR INVERSES ? never takes the same value twice, whereas ? does take on the same value twice (both 2 & 3 have the same image 4 ) In symbols, ? 2 = ?(3) but ? ? 1 ≠ ? ? 2 ? is a one to one function, while ? is not one to one
2018-2019 WS CH 2.3 Inverse Functions 3 DEFINITION OF ONE TO ONE FUNCTION A function within a domain ? is called one-to-one function if NO two elements of ? have the same image, that is ? ? 1 ≠ ? ? 2 , whenever ? 1 ≠ ? 2 An equivalent way of writing the condition for one-to- one function is If ? ? 1 = ? ? 2 , then ? 1 = ? 2
2018-2019 WS CH 2.3 Inverse Functions 4 HORIZONTAL LINE TEST A function is one-to-one if and only if no horizontal line intersects its graph more than once
2018-2019 WS CH 2.3 Inverse Functions 5 If a function is one-to-one, then the functions maps each ? to one and only one ? , and no two ? values maps to the same ? value INVERSE FUNCTIONS This means that there is one-to-one correspondence between the input (domain) and the output (range) of a one-to-one function ?(?) In the special case of one-to-one function, it would be possible to map from the output (range) back to the input (domain) and this mapping would also be a function
2018-2019 WS CH 2.3 Inverse Functions 6 The function that maps the output back to the input of a function ?

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