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Stitz-Zeager_College_Algebra_e-book

# Youll need the rational zeros theorem theorem 39 in

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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...
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