College Algebra 7th Edition

Published by Brooks Cole

Chapter 2, Functions - Section 2.8 - One-to-One Functions and their Inverses - 2.8 Exercises - Page 262: 45

Answer

f and g are inverses of each other

Work Step by Step

$g(f(x)) = g(\frac{1}{x - 1}) = \frac{1}{1 - 1} + 1 = x$ $f(g(x)) = f(\frac{1}{x} + 1 ) = \frac{1}{\frac{1}{x} + 1 -1} = \frac{1}{\frac{1}{x}} = x$ Since g(f(x)) = f(g(x)), f and g are inverses of each other

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