College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Chapter 2 Review - Exercises: 89

Answer

Yes, one-to-one.

Work Step by Step

We are given: $f(x)=3+x^{3}$ This function is one-to-one because it passes the horizontal line test (it is a shifted cubic function, which is odd). We can show this algebraically. We start with the assumption: $x_1\neq x_2$ $x_{1}^{3}\neq x_{2}^{3}$ $3+x_{1}^{3}\neq 3+x_{2}^{3}$ Because cubing unique values produces another unique value. Thus the function will not have the same $y$ value for two different $x$ values. It is therefore one-to-one.
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