Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 7 - Exponential and Logarithmic Functions - Get Ready! - Page 431: 11

Answer

$y=\pm \sqrt{ 5 - \frac{1}{2}x}$. The inverse is not a function

Work Step by Step

Firstly swap the given variables : $x=10-2 y^{2}$ Solve for $y$. Now isolate $2y^{2}$ on one side : $2y^{2}=10-x$ Divide both sides by 2 : $y^{2}=5 -\frac{1}{2}x$ Now, take the square root of the both sides : $y=\pm \sqrt{ 5 - \frac{1}{2}x}$ The inverse is not a function because, for most values of $x$, there corresponds two values of $y$.
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