MATH 041 Lecture Notes - Lecture 6: Inverse Function
Document Summary
1. 6 inverse functions f(x) = 2x 4 <========> g(x) = (x + 4)/2 x. Swap x and y to create a new function f(x) = 3x + 7 g(x) = (x 7)/3 f(2) = 6 + 7 = 13 g(13) = (13 7)/3 = 2 f(0) = 7 g(7) = 0. Inverse notation f 1 is read as f inverse: f(x) = 2x 4 f 1 (x) = (x + 4)/2. Composition of inverses f(f 1 (x)) = 2(x + 4)/2 4 = x + 4 4 = x f 1 (f(x)) = (2x 4 + 4)/2 = x 2 + 2 = x. If it"s truly the inverse, f(f 1 (x)) and f 1 (f(x)) will always be equal to x. If the horizontal line passes through more than one point of the function, then the function does not have an inverse function. Graphs of inverse functions are reflections in the line y = x.
