MAT 110 Lecture Notes - Lecture 10: Precalculus, Inverse Function, Inverse Trigonometric Functions
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Provide a generalization to each of the key terms listed in this section. 1 properties of functions and their inverses: f 1 (f (x)) = x and f (cid:0)f 1 (x)(cid:1) = x. F 1 (f (x)) = x would occur every x thats in f s domain. F (cid:0)f 1 (x)(cid:1) = x for every x thats in f 1s domain: domain and range. F s domain = f 1s range. F s range = f 1s domain: both f s and f 1s graph are symmetric, but with respect to the line y = x. If you have a function has its own inverse function, then the implicit equation of the inverse function would be x = f (y). If you are solving the given equation for y, then you would have to obtain the explicit equation that would look like y = f 1(x). Inverse sine function y = sin 1 (x) x = sin (y)
