This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: 6-2: One-to-One Functions; Inverse FunctionsIf f(x) = yis a function, its inverse f –1(x) is f(y) = x, where ybecomes the domain and xbecomes the range. If for each yin the domain of the inverse function there is a unique xin the range, it is a one-to-one function. If a horizontal lineintersects the graph of a function fno more than once, then fis one-to-one. Only one-to-one functions have inverses. We can verify that fand f–1are inverses showing thatf( f –1(x)) = f-1( f (x))= x.The graph of a function fand its inverse f –1are symmetric with respect to the line y = x.To find the inverse of a function y = f(x),interchange xand yto obtain x = f(y)and solve for yin terms of x.Find the inverse and determine whether the inverse is a function:1.[(Bob, 68), (Dave, 92), (Carol, 87), (Elaine, 74), (Chuck, 87)].Not one-to-one2.[(-2, 5), (-1, 3), (3, 7), (4, 12)One-to-onef-1(x) = [(5, -2), (3, -1), (7, 3), (12, 4)]Use the horizontal line test to see whether f is one-to-one; if yes, graph its inverse:...
View Full Document
This note was uploaded on 01/04/2012 for the course MAC 1105 taught by Professor Staff during the Fall '08 term at Miami Dade College, Miami.
- Fall '08
- Inverse Functions