Stitz-Zeager_College_Algebra_e-book

Youll need the rational zeros theorem theorem 39 in

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 5 We now use our algorithm to find j −1 (x). y y x 0 = = = = y= y= y= y= y= y= y= j (x) x2 − 2x + 4 , x ≤ 1 y 2 − 2y + 4 , y ≤ 1 y 2 − 2y + 4 − x 2 ± (−2)2 − 4(1)(4 − x) 2(1) √ 2 ± 4x − 12 2 2 ± 4(x − 3) √2 2±2 x−3 2√ 2 1± x−3 √2 1 ± √x − 3 1− x−3 switch x and y quadratic formula, c = 4 − x since y ≤ 1. √ We have j −1 (x) = 1 − x − 3. When we simplify j −1 ◦ j (x), we need to remember that the domain of j is x ≤ 1. j −1 ◦ j (x) = = = = = = = = j −1 (j (x)) j −1 x2 − 2x + 4 , x ≤ 1 1 − √ (x2 − 2x + 4) − 3 1 − x2 − 2x + 1 1 − (x − 1)2 1 − | x − 1| 1 − (−(x − 1)) since x ≤ 1 x Checking j ◦ j −1 , we get j ◦ j −1 (x) = = = = = = j j −1 (√) x j 1− x−3 √ √ 2 1− x−3 −2 1− x−3 +4 √ √ √ 2 1−2 x−3+ x−3 −2+2 x−3+4 3+x−3 x We can use what we know from Section 1.8 to graph y = j −1 (x) on the same axes as y = j (x) to get 306 Further Topics in Func...
View Full Document

This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online