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Which of the following statements is true about the function f(x) = 1/(x-3)?

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Question: Which of the following statements is true about the function f(x) = 1/(x-3)?

Options:

  1. Continuous at x = 3
  2. Continuous everywhere
  3. Not continuous at x = 3
  4. Continuous at x = 0

Correct Answer: Not continuous at x = 3

Solution: 

The function f(x) = 1/(x-3) is not defined at x = 3, hence it is not continuous at that point.

Which of the following statements is true about the function f(x) = 1/(x-3)?

Practice Questions

Q1
Which of the following statements is true about the function f(x) = 1/(x-3)?
  1. Continuous at x = 3
  2. Continuous everywhere
  3. Not continuous at x = 3
  4. Continuous at x = 0

Questions & Step-by-Step Solutions

Which of the following statements is true about the function f(x) = 1/(x-3)?
  • Step 1: Identify the function given, which is f(x) = 1/(x-3).
  • Step 2: Look for any values of x that would make the function undefined.
  • Step 3: Notice that if x = 3, the denominator (x-3) becomes 0.
  • Step 4: Since division by zero is not allowed, f(x) is not defined at x = 3.
  • Step 5: Because the function is not defined at x = 3, it cannot be continuous at that point.
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