MAC1140 Lecture Notes - Lecture 10: Inverse Trigonometric Functions, Trigonometric Functions, Inverse Function
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7. 4 inverse of the trigonometric functions notes: sterling. Provide a generalization to each of the key terms listed in this section. Properties of functions and their inverses f 1 (f (x)) = x and f (f 1 (x)) = x. The following would occur when every x is in f "s domain: The following would occur when every x is in f 1"s domain: f 1 (f (x)) = x f (cid:0)f 1 (x)(cid:1) = x. The domain of f is the range of f 1. The range of f is the domain of f 1. The graphs from both f and f 1 are actually symmetric, but it would be with respect to the line of y = x. If you have a functions has its own inverse function, then the implicit equation of the inverse function would be the following: x = f (y)