College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 3 - Section 3.5 - Rational Functions: Graphs, Applications, and Models - 3.5 Exercises: 2

Answer

Domain: all real numbers except for $x=0$. Range: all positive real numbers.

Work Step by Step

As the denominator of a fraction cannot be zero, $x\ne 0$. Apart from $x=0$ all other real numbers are allowed, therefore the domain is all real numbers, except for 0. In $f(x)=1/x^2$ the y-values will always be positive numbers, as both the numerator and the denominator are positive ( $x^2$ is always non-negative), therefore zero is excluded. The range is all positive real numbers.
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