Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 5 - Linear Functions - Concept Byte - Page 329: 4


$y = 2x - 2$

Work Step by Step

First, rewrite the equation with $f(x)$ replaced with $y$: $y = \frac{1}{2}x + 1$ To find the inverse of a function, we replace $y$ with $x$ and $x$ with $y$: $x = \frac{1}{2}y + 1$ Now we solve for $y$. First, subtract the $y$ term from each side of the equation to have $y$ terms on the left side of the equation: $x -\frac{1}{2}y = 1$ Subtract $x$ from each side of the equation to isolate the $y$ term: $-\frac{1}{2}y = - x + 1$ Divide each side by $-\frac{1}{2}$ to solve for $y$, which means we multiply by the reciprocal, which is $-2$: $y = - x(-2) + 1(-2)$ Multiply out terms to simplify: $y = 2x - 2$
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