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Course 3, Unit 8 - Inverse Functions

Overview
This unit introduces inverse functions. Logarithms and the properties of logarithms were introduced in Course 2 Unit 5 and are revisited here. Then the logarithm function as the inverse of exponential function base is studied. Students also develop an understanding of the inverse sine, cosine, and tangent functions and consider applications of these functions.

New Key Ideas from Course 3, Unit 8

  • For a given function f, if the function g has domain equal to the range of f, range equal to the domain of f, and g(f(x)) = x for all x, then g is called the inverse of f. For example, for f(x) = 2x + 4, the inverse function is g(x) = (x − 4)/2. (See pages 543-548.)

  • Logarithms: and their properties (See pages 560-566.)

  • Sine, cosine, and tangent inverse functions: (See pages 577-581 and 586-588.)

  • Trigonometric equations: finding solutions (See pages 581-583.)

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