Stitz-Zeager_College_Algebra_e-book

What is the signicance of the y intercept of the

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: tions y 6 5 y = j (x) y=x 4 3 2 1 1 2 3 4 5 6 x −1 y = j −1 (x) 2. We graph y = k (x) = √ x + 2 − 1 using what we learned in Section 1.8 and see k is one-to-one. y 2 1 −2 −1 1 2 x −1 −2 y = k (x) We now try to find k −1 . y y x x+1 (x + 1)2 2 + 2x + 1 x y = = = = = = = k (x) √ x+2−1 √ y + 2 − 1 switch x and y √ y+2 √ 2 y+2 y+2 x2 + 2 x − 1 We have k −1 (x) = x2 + 2x − 1. Based on our experience, we know something isn’t quite right. We determined k −1 is a quadratic function, and we have seen several times in this section that these are not one-to-one unless their domains are suitably restricted. Theorem 5.2 tells us that the domain of k −1 is the range of k . From the graph of k , we see that the range is [−1, ∞), which means we restrict the domain of k −1 to x ≥ −1. We now check that this works in our compositions. 5.2 Inverse Functions k −1 ◦ k (x) = = = = = = 307 k −1 (k (x)) √ x + 2 − 1 , x ≥ −2 k −1 √ √ 2 x+2−1 +2 x+2−1 −1 √ √ √ 2 x+2 −2 x+2+1+2 x+2−2−1 x+2−2 x and k ◦ k −1 (x) = = = = = = = k x2 + 2x − 1 x ≥ −1 2 √ (x + 2x − 1) + 2 − 1 2 + 2x + 1 − 1 x (x + 1)2 − 1 |x + 1| − 1 x+1−1 since x ≥ −1 x Graphically, everything checks out as well, provided that we remember the domain re...
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