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Unformatted text preview: MATH 191, Sections 1 and 3 Calculus I Fall 2007 Section 1.6: Inverse Functions If a function f is nice enough, we may just be able to define its , denoted by f- 1 . If f : A → B has the property that f ( a 1 ) = f ( a 2 ) implies a 1 = a 2 , we say that f is . This is equivalent logically to a 1 6 = a 2 implies . In case a function maps from A ⊆ R to B ⊆ R , we can recognize if it’s one-to-one from its graph. Examples. Draw the graphs of f ( x ) = x 3 , g ( x ) = sin( x ), and h ( x ) = e x in the space below. Which of these functions are one-to-one? What do they have in common? One way to check one-to-oneness using a graph is by the Horizontal Line Test . Go back to the graphs you drew above and make sure you understand how this works. Suppose now that f is one-to-one. We can define a new function as follows: if f ( a ) = b , we let g ( b ) = a . Why does rule this actually define a function? What is the domain of this new function? What is its range?...
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- Fall '07
- Inverse Functions, Inverse, Inverse function, cancellation identities