Which of the following functions is not continuous at x = 0?

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Question: Which of the following functions is not continuous at x = 0?

Options:

Correct Answer: f(x) = 1/x

Solution:

The function f(x) = 1/x is not defined at x = 0, hence it is not continuous there.

Which of the following functions is not continuous at x = 0?

Which of the following functions is not continuous at x = 0?

Step 1: Understand what continuity means. A function is continuous at a point if you can draw it without lifting your pencil at that point.
Step 2: Identify the point we are checking for continuity, which is x = 0 in this case.
Step 3: Look at the function f(x) = 1/x. Check if it is defined at x = 0.
Step 4: Notice that when you try to substitute x = 0 into the function f(x) = 1/x, you get 1/0, which is undefined.
Step 5: Since the function is not defined at x = 0, it cannot be continuous there.

No concepts available.