Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 2 - 2.7 - Inverse Functions - 2.7 Exercises - Page 230: 94


No inverse

Work Step by Step

Using the graph, determine the values of $f$ for each of the values of $x\in\{1,3,4,6\}$: $f(-4)=3$ $f(-2)=4$ $f(0)=0$ $f(3)=-1$ So we have the points: $(-4,3),(-2,4),(0,0),(3,-1)$ Check if the given function $f$ passes the Horizontal Line Test: we notice that there is a horizontal line which intersects the graph at more than one point; therefore the function fails the test, so it has no inverse. If $(a,b)$ belongs to the graph of $f$, then $(b,a)$ belongs to the graph of $f^{-1}$. In order to determine the inverse $f^{-1}(x)$ we consider the ordered pairs: $(1,1),(2,3),(6,4),(7,6)$ Plot the points and join them by segments to graph $f^{-1}$:
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