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Inverse Functions Rita Korsunsky
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Definition x f(x) b f(b) a f(a) R D Definition
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Horizontal Line Test If the graph of a function y = f(x) is such that no horizontal line intersects the graph in more than one point ,then it is one to one and has an inverse function. One-to-one function. Has an inverse function Not one-to-one. Has no inverse function
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Definitions Example 1 f(x) and g(x) are inverse functions if :
1) g(f(x)) = x for all x in the domain of f 2) f(g(x)) = x for all x in the domain of g Example 1
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For every point (a,b) on the graph of f
the point (b,a) is on the the graph of f-1 The graph of f-1 is the reflection of graph of f in line y= x
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Example 2
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Example 3
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Guidelines for finding ƒ-1
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Theorems
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prove: Derivatives of Inverse functions (slopes of tangents) are reciprocals of each other at the points where domain x and range y are interchanged(scroll down to see slopes calculated)
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Example
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Example (when g(2) is not given)
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Another proof(optional)
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