Precalc0108to0109-page17

Precalc0108to0109-page17 - On the graph of g above, the...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
(Section 1.9: Inverses of One-to-One Functions) 1.9.7 Example 4 (A One-to-One Function: Squaring Function on a Restricted Domain; Modifying Example 3) Let gx () = x 2 on the restricted domain 0, ± ² ³ ) . The graph of y = gx () below passes the Vertical Line Test (VLT) and also the Horizontal Line Test (HLT) . Consequently, g is a one-to-one correspondence between Dom g () , the set of input x values, and Range g () , the set of output y values. (Think of matched pairs .) Also, ga () = gc () ± a 2 = c 2 ± a = c , since only nonnegative inputs are allowed. • If we solve the equation gx () = 9 , or x 2 = 9 x ± 0 () , we obtain a unique solution for x , namely 3. It is the unique input that yields 9.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: On the graph of g above, the only point with y-coordinate 9 has x-coordinate 3. More generally, g x ( ) = b has a unique solution for x , the unique input that yields b , whenever b is in Range g ( ) , which is 0, ) . We can define a unique inverse function g 1 . Let Dom g 1 ( ) = Range g ( ) , which is 0, ) . Define g 1 b ( ) to be the unique solution to g x ( ) = b , for every b in Dom g 1 ( ) . For instance, g 1 9 ( ) = 3 . (In Example 1, since f ( ) = 32 , we reverse the arrow and define f 1 32 ( ) to be 0.)...
View Full Document

This document was uploaded on 12/29/2011.

Ask a homework question - tutors are online