Calculus (3rd Edition)

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

Chapter 1 - Precalculus Review - 1.1 Real Numbers, Functions, and Graphs - Exercises - Page 10: 47


The domain is all real numbers besides 0. The range is $ y \gt 0 $.

Work Step by Step

Because the function has the x variable in the denominator, and valid fractions cannot have 0 in the denominator, 0 is not included in the function's domain. Because the x in the denominator is squared, the denominator will only be positive values. Since the numerator 1 is a positive value, divided by another positive value in the denominator, our range will only include other positive values. Our range cannot include 0, because the numerator of the fraction is 1, and will never equal 0.
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