Algebra 2 Common Core

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

Chapter 8 - Rational Functions - 8-1 Inverse Variation - Practice and Problem-Solving Exercises - Page 505: 48

Answer

Inverse: $y=\pm\sqrt{\dfrac{x-5}{4}}$ The inverse is not a function.

Work Step by Step

To find the inverse of the given function, perform the following steps: (1) Interchange the variables $x$ and $y$: $x=4y^2+5$ (2) Solve for $y$ \begin{align*} x-5&=4y^2\\\\ \frac{x-5}{4}&=y^2\\\\ \pm\sqrt{\frac{x-5}{4}}&=y \end{align*} Thus, the inverse of the given function is $y=\pm\sqrt{\dfrac{x-5}{4}}$. Since for every value of $x$, there corresponds two different values of $y$, then the inverse is NOT a function.
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