Understanding Continuity: When is a Function Continuous?

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A function f(x)/g(x) is continuous when g(x) is defined and does not equal zero. The confusion arises from the interpretation of "defined," which means having a value rather than being non-zero. The key point is that a function is undefined if its denominator equals zero, making option b) the correct choice. Understanding the conditions for continuity is essential for solving related problems. Clarification on these definitions helps in grasping the concept of continuity in functions.
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Homework Statement



You're simply given f(x)/g(x) and it asks, when is the function continuous?

There was one that was definitely wrong, so I remember these remaining choices:
a) It is continuous when f(x) and g(x) are defined
b) " " when g(x) cannot equal 0
c) " " when g(x) is defined.

The Attempt at a Solution



I chose c) but I realized that it could be b) because you can't have a denominator 0. At the time, I was thinking that defined meant having a value that is not 0 because usually when a function has a denominator 0, we call the function "undefined."

Can someone please clarify? :)
 
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The answer is b. "Defined" just means that a function has a value.
 

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