Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - 1.3 The Basic Classes of Functions - Exercises - Page 23: 26


See the proof below.

Work Step by Step

We can rewrite $ f(x)$ as follows $$ f(x)=x^2+\frac{3}{x}=\frac{x^3+3}{x}$$ which is a quotient of polynomials; that is, $ f(x)$ is rational. Also, for $ g(x)$, we have $$ g(x)=3x^3-9x+\frac{1}{x^2}=\frac{3x^5-9x^3+1}{x^2}$$ which is a quotient of polynomials; that is, $ g(x)$ is rational.
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