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6.1 Inverse Functions

# 6.1 Inverse Functions - Inverse Functions 1 If f is...

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Inverse Functions Section 6.1

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Reflective Property of Inverse Functions The graph of f contains the point (a, b) iff the graph of f -1 contains the point (b, a)
The Existence of an Inverse Function 1. A function has an inverse iff it is one-to-one. 2. If f is strictly monotonic on its entire domain, then it is one-to-one and therefore has an inverse. Use horizontal line test to determine if a function has an inverse.

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Guidelines for Finding the Inverse of a Function 1. Determine whether the function has an inverse. 2. Solve for x as a function of y. 3. Interchange x and y. 4. Define the domain of f -1 to be the range of f . 5. Verify that f(f -1(x))= x and f -1(f(x))=x
Continuity and Differentiability of

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Unformatted text preview: Inverse Functions 1. If f is continuous on its domain, then f -1 is continuous on its domain. 2. If f is increasing on its domain, then f -1 is increasing on its domain. 3. If f is decreasing on its domain, then f -1 is decreasing on its domain. 4. If f is differentiable at c and f -1(c) = 0, then f -1 is differentiable at f(c). The Derivative of an Inverse Function Graphs of inverse functions have reciprocal slopes at points (a, b) and (b, a). Joke Time What do cats eat for breakfast? Mice Krispies What did the canary say when its new cage fell apart? CHEEP CHEEP Where does a sheep go to get a hair cut? To the baa baa shop!...
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6.1 Inverse Functions - Inverse Functions 1 If f is...

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