College Algebra 7th Edition

Published by Brooks Cole

Chapter 2, Functions - Section 2.8 - One-to-One Functions and their Inverses - 2.8 Exercises: 47

Answer

The two functions are inverses to each other

Work Step by Step

$f(x) = \frac{x + 2}{x - 2}$ Find the inverse $y = \frac{x + 2}{x - 2}$ y(x - 2) = x + 2 yx - 2y = x + 2 yx - x = 2 + 2y x(y - 1) = 2 + 2y $x = \frac{2 + 2y }{(y - 1)}$ $f^{-1}(x) = \frac{2 + 2x }{(x - 1)} = g(x)$ $g(x) = \frac{2x +2}{x - 1}$ Find the inverse $y= \frac{2x +2}{x - 1}$ y(x - 1) = 2x + 2 yx - y = 2x + 2 yx - 2x = 2 + y x(y - 2) = 2 + y $x = \frac{2 + y}{y - 2}$ $g^{-1}(x) = \frac{2 + x}{x- 2} = f(x)$ The two functions are inverses to each other

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