Algebra and Trigonometry: Structure and Method, Book 2
Algebra and Trigonometry: Structure and Method, Book 2
2000th Edition
ISBN: 9780395977255
Author: MCDOUGAL LITTEL
Publisher: McDougal Littell
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Chapter 10.3, Problem 7OE
To determine

Whether h−1(x) exists or not if h(x)=x2+2 .

Expert Solution & Answer
Check Mark

Answer to Problem 7OE

The inverse of h(x)=x2+2 which is h−1(x) does not exist.

Explanation of Solution

Given information: The given function is,

  h(x)=x2+2 ....(1)

Calculation: From (1) the function will represent a parabola opening upwards. And it will not pass the horizontal line test if a horizontal line is drawn parallel to (x) axis because it will cut the graph of (1) at two distinct points as parabola is symmetric about its axis of symmetry. Hence the inverse of the function does not exist. Also we evaluate the inverse for (1), it will two values for inverse which is not possible.

For the given function h(x)=x2+2 , the inverse is evaluated as,

  y=x2+2......(Plugging h(x)=y)(x)=(y)2+2......(Exchanging variables)y=±x−2......(Solving for variable (y))h−1(x)=±x−2......(Plugging y=h−1(x))

Again there are two values for h−1(x) . Therefore h−1(x) does not exist.

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Chapter 10.3, Problem 6OE
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Chapter 10.3, Problem 1WE

Chapter 10 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 10.1 - Prob. 1OECh. 10.1 - Prob. 2OECh. 10.1 - Prob. 3OECh. 10.1 - Prob. 4OECh. 10.1 - Prob. 5OECh. 10.1 - Prob. 6OECh. 10.1 - Prob. 7OECh. 10.1 - Prob. 8OECh. 10.1 - Prob. 9OECh. 10.1 - Prob. 10OE
Ch. 10.1 - Prob. 11OECh. 10.1 - Prob. 12OECh. 10.1 - Prob. 13OECh. 10.1 - Prob. 14OECh. 10.1 - Prob. 15OECh. 10.1 - Prob. 16OECh. 10.1 - Prob. 17OECh. 10.1 - Prob. 18OECh. 10.1 - Prob. 19OECh. 10.1 - Prob. 20OECh. 10.1 - Prob. 21OECh. 10.1 - Prob. 22OECh. 10.1 - Prob. 23OECh. 10.1 - Prob. 24OECh. 10.1 - Prob. 25OECh. 10.1 - Prob. 26OECh. 10.1 - Prob. 27OECh. 10.1 - Prob. 28OECh. 10.1 - Prob. 29OECh. 10.1 - Prob. 30OECh. 10.1 - Prob. 31OECh. 10.1 - Prob. 1WECh. 10.1 - Prob. 2WECh. 10.1 - Prob. 3WECh. 10.1 - Prob. 4WECh. 10.1 - Prob. 5WECh. 10.1 - Prob. 6WECh. 10.1 - Prob. 7WECh. 10.1 - Prob. 8WECh. 10.1 - Prob. 9WECh. 10.1 - Prob. 10WECh. 10.1 - Prob. 11WECh. 10.1 - Prob. 12WECh. 10.1 - Prob. 13WECh. 10.1 - Prob. 14WECh. 10.1 - Prob. 15WECh. 10.1 - Prob. 16WECh. 10.1 - Prob. 17WECh. 10.1 - Prob. 18WECh. 10.1 - Prob. 19WECh. 10.1 - Prob. 20WECh. 10.1 - Prob. 21WECh. 10.1 - Prob. 22WECh. 10.1 - Prob. 23WECh. 10.1 - Prob. 24WECh. 10.1 - Prob. 25WECh. 10.1 - Prob. 26WECh. 10.1 - Prob. 27WECh. 10.1 - Prob. 28WECh. 10.1 - Prob. 29WECh. 10.1 - Prob. 30WECh. 10.1 - Prob. 31WECh. 10.1 - Prob. 32WECh. 10.1 - Prob. 33WECh. 10.1 - Prob. 34WECh. 10.1 - Prob. 35WECh. 10.1 - Prob. 36WECh. 10.1 - Prob. 37WECh. 10.1 - Prob. 38WECh. 10.1 - Prob. 39WECh. 10.1 - Prob. 40WECh. 10.1 - Prob. 41WECh. 10.1 - Prob. 42WECh. 10.1 - Prob. 43WECh. 10.1 - Prob. 44WECh. 10.1 - Prob. 45WECh. 10.1 - Prob. 46WECh. 10.1 - Prob. 47WECh. 10.1 - Prob. 48WECh. 10.1 - Prob. 49WECh. 10.1 - Prob. 50WECh. 10.1 - Prob. 1MRECh. 10.1 - Prob. 2MRECh. 10.1 - Prob. 3MRECh. 10.1 - Prob. 4MRECh. 10.1 - Prob. 5MRECh. 10.1 - Prob. 6MRECh. 10.2 - Prob. 1OECh. 10.2 - Prob. 2OECh. 10.2 - Prob. 3OECh. 10.2 - Prob. 4OECh. 10.2 - Prob. 5OECh. 10.2 - Prob. 6OECh. 10.2 - Prob. 7OECh. 10.2 - Prob. 8OECh. 10.2 - Prob. 9OECh. 10.2 - Prob. 10OECh. 10.2 - Prob. 11OECh. 10.2 - Prob. 12OECh. 10.2 - Prob. 1WECh. 10.2 - Prob. 2WECh. 10.2 - Prob. 3WECh. 10.2 - Prob. 4WECh. 10.2 - Prob. 5WECh. 10.2 - Prob. 6WECh. 10.2 - Prob. 7WECh. 10.2 - Prob. 8WECh. 10.2 - Prob. 9WECh. 10.2 - Prob. 10WECh. 10.2 - Prob. 11WECh. 10.2 - Prob. 12WECh. 10.2 - Prob. 13WECh. 10.2 - Prob. 14WECh. 10.2 - Prob. 15WECh. 10.2 - Prob. 16WECh. 10.2 - Prob. 17WECh. 10.2 - Prob. 18WECh. 10.2 - Prob. 19WECh. 10.2 - Prob. 20WECh. 10.2 - Prob. 21WECh. 10.2 - Prob. 22WECh. 10.2 - Prob. 23WECh. 10.2 - Prob. 24WECh. 10.2 - Prob. 25WECh. 10.2 - Prob. 26WECh. 10.2 - Prob. 27WECh. 10.2 - Prob. 28WECh. 10.2 - Prob. 29WECh. 10.2 - Prob. 30WECh. 10.2 - Prob. 31WECh. 10.2 - Prob. 32WECh. 10.2 - Prob. 33WECh. 10.2 - Prob. 34WECh. 10.2 - Prob. 35WECh. 10.2 - Prob. 36WECh. 10.2 - Prob. 37WECh. 10.2 - Prob. 38WECh. 10.2 - Prob. 39WECh. 10.3 - Prob. 1OECh. 10.3 - Prob. 2OECh. 10.3 - Prob. 3OECh. 10.3 - Prob. 4OECh. 10.3 - Prob. 5OECh. 10.3 - Prob. 6OECh. 10.3 - Prob. 7OECh. 10.3 - Prob. 1WECh. 10.3 - Prob. 2WECh. 10.3 - Prob. 3WECh. 10.3 - Prob. 4WECh. 10.3 - Prob. 5WECh. 10.3 - Prob. 6WECh. 10.3 - Prob. 7WECh. 10.3 - Prob. 8WECh. 10.3 - Prob. 9WECh. 10.3 - Prob. 10WECh. 10.3 - Prob. 11WECh. 10.3 - Prob. 12WECh. 10.3 - Prob. 13WECh. 10.3 - Prob. 14WECh. 10.3 - Prob. 15WECh. 10.3 - Prob. 16WECh. 10.3 - Prob. 17WECh. 10.3 - Prob. 18WECh. 10.3 - Prob. 19WECh. 10.3 - Prob. 20WECh. 10.3 - Prob. 21WECh. 10.3 - Prob. 22WECh. 10.3 - Prob. 23WECh. 10.3 - Prob. 24WECh. 10.3 - Prob. 25WECh. 10.3 - Prob. 26WECh. 10.3 - Prob. 1MRECh. 10.3 - Prob. 2MRECh. 10.3 - Prob. 3MRECh. 10.3 - Prob. 4MRECh. 10.3 - Prob. 5MRECh. 10.3 - Prob. 6MRECh. 10.3 - Prob. 7MRECh. 10.3 - Prob. 8MRECh. 10.3 - Prob. 9MRECh. 10.3 - Prob. 10MRECh. 10.3 - Prob. 11MRECh. 10.3 - Prob. 12MRECh. 10.3 - Prob. 1STCh. 10.3 - Prob. 2STCh. 10.3 - Prob. 3STCh. 10.3 - Prob. 4STCh. 10.3 - Prob. 5STCh. 10.3 - Prob. 6STCh. 10.3 - Prob. 7STCh. 10.4 - Prob. 1OECh. 10.4 - Prob. 2OECh. 10.4 - Prob. 3OECh. 10.4 - Prob. 4OECh. 10.4 - Prob. 5OECh. 10.4 - Prob. 6OECh. 10.4 - Prob. 7OECh. 10.4 - Prob. 8OECh. 10.4 - Prob. 9OECh. 10.4 - Prob. 10OECh. 10.4 - Prob. 11OECh. 10.4 - Prob. 12OECh. 10.4 - Prob. 13OECh. 10.4 - Prob. 14OECh. 10.4 - Prob. 15OECh. 10.4 - Prob. 16OECh. 10.4 - Prob. 17OECh. 10.4 - Prob. 18OECh. 10.4 - Prob. 19OECh. 10.4 - Prob. 20OECh. 10.4 - Prob. 1WECh. 10.4 - Prob. 2WECh. 10.4 - Prob. 3WECh. 10.4 - Prob. 4WECh. 10.4 - Prob. 5WECh. 10.4 - Prob. 6WECh. 10.4 - Prob. 7WECh. 10.4 - Prob. 8WECh. 10.4 - Prob. 9WECh. 10.4 - Prob. 10WECh. 10.4 - Prob. 11WECh. 10.4 - Prob. 12WECh. 10.4 - Prob. 13WECh. 10.4 - Prob. 14WECh. 10.4 - Prob. 15WECh. 10.4 - Prob. 16WECh. 10.4 - Prob. 17WECh. 10.4 - Prob. 18WECh. 10.4 - Prob. 19WECh. 10.4 - Prob. 20WECh. 10.4 - Prob. 21WECh. 10.4 - Prob. 22WECh. 10.4 - Prob. 23WECh. 10.4 - Prob. 24WECh. 10.4 - Prob. 25WECh. 10.4 - Prob. 26WECh. 10.4 - Prob. 27WECh. 10.4 - Prob. 28WECh. 10.4 - Prob. 29WECh. 10.4 - Prob. 30WECh. 10.4 - Prob. 31WECh. 10.4 - Prob. 32WECh. 10.4 - Prob. 33WECh. 10.4 - Prob. 34WECh. 10.4 - Prob. 35WECh. 10.4 - Prob. 36WECh. 10.4 - Prob. 37WECh. 10.4 - Prob. 38WECh. 10.4 - Prob. 39WECh. 10.4 - Prob. 40WECh. 10.4 - Prob. 41WECh. 10.4 - Prob. 42WECh. 10.4 - Prob. 43WECh. 10.5 - Prob. 1OECh. 10.5 - Prob. 2OECh. 10.5 - Prob. 3OECh. 10.5 - Prob. 4OECh. 10.5 - Prob. 5OECh. 10.5 - Prob. 6OECh. 10.5 - Prob. 7OECh. 10.5 - Prob. 8OECh. 10.5 - Prob. 9OECh. 10.5 - Prob. 10OECh. 10.5 - Prob. 11OECh. 10.5 - Prob. 12OECh. 10.5 - Prob. 13OECh. 10.5 - Prob. 14OECh. 10.5 - Prob. 15OECh. 10.5 - Prob. 16OECh. 10.5 - Prob. 17OECh. 10.5 - Prob. 18OECh. 10.5 - Prob. 19OECh. 10.5 - Prob. 20OECh. 10.5 - Prob. 21OECh. 10.5 - Prob. 22OECh. 10.5 - Prob. 23OECh. 10.5 - Prob. 24OECh. 10.5 - Prob. 1WECh. 10.5 - Prob. 2WECh. 10.5 - Prob. 3WECh. 10.5 - Prob. 4WECh. 10.5 - Prob. 5WECh. 10.5 - Prob. 6WECh. 10.5 - Prob. 7WECh. 10.5 - Prob. 8WECh. 10.5 - Prob. 9WECh. 10.5 - Prob. 10WECh. 10.5 - Prob. 11WECh. 10.5 - Prob. 12WECh. 10.5 - Prob. 13WECh. 10.5 - Prob. 14WECh. 10.5 - Prob. 15WECh. 10.5 - Prob. 16WECh. 10.5 - Prob. 17WECh. 10.5 - Prob. 18WECh. 10.5 - Prob. 19WECh. 10.5 - Prob. 20WECh. 10.5 - Prob. 21WECh. 10.5 - Prob. 22WECh. 10.5 - Prob. 23WECh. 10.5 - Prob. 24WECh. 10.5 - Prob. 25WECh. 10.5 - Prob. 26WECh. 10.5 - Prob. 27WECh. 10.5 - Prob. 28WECh. 10.5 - Prob. 29WECh. 10.5 - Prob. 30WECh. 10.5 - Prob. 31WECh. 10.5 - Prob. 32WECh. 10.5 - Prob. 33WECh. 10.5 - Prob. 34WECh. 10.5 - Prob. 35WECh. 10.5 - Prob. 36WECh. 10.5 - Prob. 37WECh. 10.5 - Prob. 38WECh. 10.5 - Prob. 39WECh. 10.5 - Prob. 40WECh. 10.5 - Prob. 41WECh. 10.5 - Prob. 42WECh. 10.5 - Prob. 43WECh. 10.5 - Prob. 44WECh. 10.5 - Prob. 45WECh. 10.5 - Prob. 46WECh. 10.5 - Prob. 47WECh. 10.5 - Prob. 48WECh. 10.5 - Prob. 49WECh. 10.5 - Prob. 50WECh. 10.5 - Prob. 51WECh. 10.5 - Prob. 1MRECh. 10.5 - Prob. 2MRECh. 10.5 - Prob. 3MRECh. 10.5 - Prob. 4MRECh. 10.5 - Prob. 5MRECh. 10.5 - Prob. 6MRECh. 10.5 - Prob. 7MRECh. 10.5 - Prob. 8MRECh. 10.5 - Prob. 9MRECh. 10.5 - Prob. 10MRECh. 10.5 - Prob. 11MRECh. 10.5 - Prob. 12MRECh. 10.5 - Prob. 13MRECh. 10.5 - Prob. 1STCh. 10.5 - Prob. 2STCh. 10.5 - Prob. 3STCh. 10.5 - Prob. 4STCh. 10.5 - Prob. 5STCh. 10.5 - Prob. 6STCh. 10.5 - Prob. 7STCh. 10.6 - Prob. 1OECh. 10.6 - Prob. 2OECh. 10.6 - Prob. 3OECh. 10.6 - Prob. 4OECh. 10.6 - Prob. 5OECh. 10.6 - Prob. 6OECh. 10.6 - Prob. 7OECh. 10.6 - Prob. 8OECh. 10.6 - Prob. 9OECh. 10.6 - Prob. 10OECh. 10.6 - Prob. 11OECh. 10.6 - Prob. 12OECh. 10.6 - Prob. 13OECh. 10.6 - Prob. 14OECh. 10.6 - Prob. 15OECh. 10.6 - Prob. 16OECh. 10.6 - Prob. 1WECh. 10.6 - Prob. 2WECh. 10.6 - Prob. 3WECh. 10.6 - Prob. 4WECh. 10.6 - Prob. 5WECh. 10.6 - Prob. 6WECh. 10.6 - Prob. 7WECh. 10.6 - Prob. 8WECh. 10.6 - Prob. 9WECh. 10.6 - Prob. 10WECh. 10.6 - Prob. 11WECh. 10.6 - Prob. 12WECh. 10.6 - Prob. 13WECh. 10.6 - Prob. 14WECh. 10.6 - Prob. 15WECh. 10.6 - Prob. 16WECh. 10.6 - Prob. 17WECh. 10.6 - Prob. 18WECh. 10.6 - Prob. 19WECh. 10.6 - Prob. 20WECh. 10.6 - Prob. 21WECh. 10.6 - Prob. 22WECh. 10.6 - Prob. 23WECh. 10.6 - Prob. 24WECh. 10.6 - Prob. 25WECh. 10.6 - Prob. 26WECh. 10.6 - Prob. 27WECh. 10.6 - Prob. 28WECh. 10.6 - Prob. 29WECh. 10.6 - Prob. 30WECh. 10.6 - Prob. 31WECh. 10.6 - Prob. 32WECh. 10.6 - Prob. 33WECh. 10.6 - Prob. 34WECh. 10.6 - Prob. 35WECh. 10.6 - Prob. 36WECh. 10.6 - Prob. 37WECh. 10.6 - Prob. 38WECh. 10.6 - Prob. 39WECh. 10.6 - Prob. 40WECh. 10.6 - Prob. 41WECh. 10.6 - Prob. 42WECh. 10.7 - Prob. 1OECh. 10.7 - Prob. 2OECh. 10.7 - Prob. 3OECh. 10.7 - Prob. 4OECh. 10.7 - Prob. 1PCh. 10.7 - Prob. 2PCh. 10.7 - Prob. 3PCh. 10.7 - Prob. 4PCh. 10.7 - Prob. 5PCh. 10.7 - Prob. 6PCh. 10.7 - Prob. 7PCh. 10.7 - Prob. 8PCh. 10.7 - Prob. 9PCh. 10.7 - Prob. 10PCh. 10.7 - Prob. 11PCh. 10.7 - Prob. 12PCh. 10.7 - Prob. 13PCh. 10.7 - Prob. 14PCh. 10.7 - Prob. 15PCh. 10.7 - Prob. 16PCh. 10.7 - Prob. 17PCh. 10.7 - Prob. 18PCh. 10.7 - Prob. 19PCh. 10.7 - Prob. 20PCh. 10.7 - Prob. 21PCh. 10.7 - Prob. 22PCh. 10.7 - Prob. 1MRECh. 10.7 - Prob. 2MRECh. 10.7 - Prob. 3MRECh. 10.7 - Prob. 4MRECh. 10.7 - Prob. 5MRECh. 10.7 - Prob. 6MRECh. 10.7 - Prob. 7MRECh. 10.7 - Prob. 8MRECh. 10.7 - Prob. 9MRECh. 10.7 - Prob. 10MRECh. 10.7 - Prob. 11MRECh. 10.7 - Prob. 12MRECh. 10.8 - Prob. 1OECh. 10.8 - Prob. 2OECh. 10.8 - Prob. 3OECh. 10.8 - Prob. 4OECh. 10.8 - Prob. 5OECh. 10.8 - Prob. 6OECh. 10.8 - Prob. 7OECh. 10.8 - Prob. 8OECh. 10.8 - Prob. 9OECh. 10.8 - Prob. 10OECh. 10.8 - Prob. 11OECh. 10.8 - Prob. 12OECh. 10.8 - Prob. 13OECh. 10.8 - Prob. 14OECh. 10.8 - Prob. 15OECh. 10.8 - Prob. 16OECh. 10.8 - Prob. 1WECh. 10.8 - Prob. 2WECh. 10.8 - Prob. 3WECh. 10.8 - Prob. 4WECh. 10.8 - Prob. 5WECh. 10.8 - Prob. 6WECh. 10.8 - Prob. 7WECh. 10.8 - Prob. 8WECh. 10.8 - Prob. 9WECh. 10.8 - Prob. 10WECh. 10.8 - Prob. 11WECh. 10.8 - Prob. 12WECh. 10.8 - Prob. 13WECh. 10.8 - Prob. 14WECh. 10.8 - Prob. 15WECh. 10.8 - Prob. 16WECh. 10.8 - Prob. 17WECh. 10.8 - Prob. 18WECh. 10.8 - Prob. 19WECh. 10.8 - Prob. 20WECh. 10.8 - Prob. 21WECh. 10.8 - Prob. 22WECh. 10.8 - Prob. 23WECh. 10.8 - Prob. 24WECh. 10.8 - Prob. 25WECh. 10.8 - Prob. 26WECh. 10.8 - Prob. 27WECh. 10.8 - Prob. 28WECh. 10.8 - Prob. 29WECh. 10.8 - Prob. 30WECh. 10.8 - Prob. 31WECh. 10.8 - Prob. 32WECh. 10.8 - Prob. 33WECh. 10.8 - Prob. 34WECh. 10.8 - Prob. 35WECh. 10.8 - Prob. 36WECh. 10.8 - Prob. 37WECh. 10.8 - Prob. 38WECh. 10.8 - Prob. 39WECh. 10.8 - Prob. 40WECh. 10.8 - Prob. 41WECh. 10.8 - Prob. 42WECh. 10.8 - Prob. 43WECh. 10.8 - Prob. 44WECh. 10.8 - Prob. 45WECh. 10.8 - Prob. 46WECh. 10.8 - Prob. 47WECh. 10.8 - Prob. 48WECh. 10.8 - Prob. 49WECh. 10.8 - Prob. 50WECh. 10.8 - Prob. 51WECh. 10.8 - Prob. 1STCh. 10.8 - Prob. 2STCh. 10.8 - Prob. 3STCh. 10.8 - Prob. 4STCh. 10.8 - Prob. 5STCh. 10.8 - Prob. 1ECh. 10.8 - Prob. 2ECh. 10.8 - Prob. 3ECh. 10 - Prob. 1CRCh. 10 - Prob. 2CRCh. 10 - Prob. 3CRCh. 10 - Prob. 4CRCh. 10 - Prob. 5CRCh. 10 - Prob. 6CRCh. 10 - Prob. 7CRCh. 10 - Prob. 8CRCh. 10 - Prob. 9CRCh. 10 - Prob. 10CRCh. 10 - Prob. 11CRCh. 10 - Prob. 12CRCh. 10 - Prob. 13CRCh. 10 - Prob. 14CRCh. 10 - Prob. 15CRCh. 10 - Prob. 16CRCh. 10 - Prob. 1CTCh. 10 - Prob. 2CTCh. 10 - Prob. 3CTCh. 10 - Prob. 4CTCh. 10 - Prob. 5CTCh. 10 - Prob. 6CTCh. 10 - Prob. 7CTCh. 10 - Prob. 8CTCh. 10 - Prob. 9CTCh. 10 - Prob. 10CTCh. 10 - Prob. 11CTCh. 10 - Prob. 12CTCh. 10 - Prob. 13CTCh. 10 - Prob. 1MPSCh. 10 - Prob. 2MPSCh. 10 - Prob. 3MPSCh. 10 - Prob. 4MPSCh. 10 - Prob. 5MPSCh. 10 - Prob. 6MPSCh. 10 - Prob. 7MPSCh. 10 - Prob. 8MPSCh. 10 - Prob. 9MPSCh. 10 - Prob. 10MPSCh. 10 - Prob. 11MPSCh. 10 - Prob. 12MPSCh. 10 - Prob. 13MPS

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