Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 2 - Section 2.6 - Function Notation and Linear Functions - 2.6 Exercises: 32

Answer

$-\frac{1}{x^{2}}+\frac{4}{x}+1$

Work Step by Step

We are given that $g(x)=-x^{2}+4x+1$. In order to evaluate the function at $\frac{1}{x}$, we can plug in $\frac{1}{x}$ to the function and evaluate directly. $g(\frac{1}{x})=-(\frac{1}{x})^{2}+4(\frac{1}{x})+1=-(\frac{1}{x^{2}})+\frac{4}{x}+1=-\frac{1}{x^{2}}+\frac{4}{x}+1$
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