MATH 104 Chapter : Review of Inverses

• School: UBC
• Department: Mathematics
• Course: MATH 104
• Professor: Thomas Hughes

Document Summary

Function f maps values from its domain d to its range r. The more of f to a function f-1 that undoes f f-1 = (f(x)) = x f-1 has domain r and range d f(x) = y f-1(y) = x. A function is one-to-one on the domain if each value of f(x) corresponds to exactly one x defines d. No two points on d are mapped on the same point. (horizontal line. Ex. f(x) = ex ex is one-to-one on all rational numbers (d= all rational numbers) Horizontal line test: a horizontal is one-to-one if any horizontal line intersects the graph at most once. Ex. f(x) = sin (x) on d = [0, ] test. Theorem: a one-to-one function f on a domian d with range r has an inverse. (with domain r and range d) Computing inverses: solve y = f(x) for x, swith x and y, write y = f-1 (x)