Answer
The function is continuous for all real numbers and has no discontinuities.
Work Step by Step
By Theorem $1.11$:
Since both $3x$ and $\cos{x}$ are continuous for all real numbers, $3x-\cos{x}$ is continuous.
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
Published by
Brooks Cole
ISBN 10:
1-28505-709-0
ISBN 13:
978-1-28505-709-5
Chapter 1 - Limits and Their Properties - 1.4 Exercises - Page 80: 41
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