Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 1: Functions - Section 1.1 - Functions and Their Graphs - Exercises 1.1: 5

Answer

The domain is $(-\infty,3)\cup(3,\infty)$ The range is $(-\infty,0)\cup(0,\infty)$

Work Step by Step

$f(t)=\frac{4}{3-t}$ $3-t\neq0$ - Because we can't divide by 0 $t \neq -3$ The domain is $(-\infty,3)\cup(3,\infty)$ When $t<3$, we know that $3-t>0$ and therefore $\frac{4}{3-t}>0$. When $t>3$, we know that $3-t<0$ and therefore $\frac{4}{3-t}<0$. This means $t$ can be any real number except $0$, which makes the range $(-\infty,0)\cup(0,\infty)$.
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